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# Solving quadratics by taking square roots: with steps

Sal discusses the exact order of steps in the process of solving the equation 3(x+6)^2=75. Created by Sal Khan.

## Want to join the conversation?

• Do we have to write the plus or minus signs?
• Miles,
When you take the square root of both sides of an equation, you get two answers.
(x+6)²=25 Take the square root of both sides
x+6 = ±√25
x+6=±5
The plus or minus sign means you have two equations
x+6 = 5 and x+6 = -5
You don't have to write the ± sign but if you don't, you then need to write out both equations x+6 = 5 and x+6 = -5 and then solve each equation to get your two answers.
The ± sign is used to indicate that you have two equations you are solving at the same time.

I hope that helps make it click for you.
• how to find roots of a quadratic equation if b^2-4ac < 0 , if b^2-4ac is a perfect square i.e. (-64) .
• Undefined. Undefined because sqrt(<0) is undefined.
• It seems that the exercise for this video is missing. Can someone tell me where these exercises are located?
• It would be in "Algebra">"Quadratic Equations">"Solving Quadratics by Taking Square Root" and all the way at the bottom is "Understanding the Equation Solving Process" where a problem like this should appear.
• At , why is it -6 plus or minus 5 instead of 5 plus or minus -6?
• You started with `x+6=±5`, so subtracting 6 from both sides yields `x=-6±5`.

If you started with `x+6=+5 or x+6=-5` and subtracted 6 from both sides, you'd get `x=-6+5 or x=-6-5`. And you could recombine those last two possibility back to just `x=-6±5`. So it's the same thing either way: the `±` sign is attached to the 5.
• Is it okay if we just put the steps and ignore figuring out the exact answer?
• Yes. Sal figured out the exact answer just for extra instruction.
• How would you solve:
h(x) = -3(x-2)(x+2)

I am found the vertices x=2 and x= -2, but I am not sure how to find the axis of symmetry, AKA the maximum or minimum. PLEASE HELP!!
• to find the x-coordinate of the vertex (which is also the axis of symmetry):
1. first find the 2 x-intercepts(when y=0)-> (x[1],0) (x[2],0)
2.add the x values of the x-intercepts then divide them by 2 -> (x[1]+x[2])/2
In your question the x-intercepts are (2,0)(-2,0)
(2+-2)/2 = 0/2 = 0
so the x-coordinate of the vertex and the axis of symmetry is 0
To find the max/min value we need to find the y- coordinate of the vertex
to do that we substitute the x coordinate of the vertex in the equation
-> h(0)=-3(0-2)(0+2)
h(0)= -3(-2)(2)
h(0)= -3(-4)
h(0)= -12
so the vertex is (0,12)
and the max value(it has a maximum value because it opens down) is 12
• on the options shown on the question, Sal chooses a "take the square root of both sides" option. not to make myself dumb if it's too obvious, but i fail to see the difference between "square both sides" and "take the square root of both sides". HEELLP!
• They are opposite operations.
If you square 4, then you are doing 4^2 = 4*4 = 16
If you take the square root of 4, then you are doing sqrt(4) = 2
Do you see the difference?

If Sal had squared both sides of: (x+6)^2=25, here's what would have happened:
[(x+6)^2]^2 = 25^2
(x+6)^4 = 625
Squaring both sides just makes the equation even more complicated.

Hope this helps.
• I understand the reason Sal is putting +/- in front of the square rooted number. However why is it that we do this only in quadratics and not other equations?
• Quadratics are not the only place where the +/- is used. We may be using functions like absolute value. But of the not-so-many places in math where the +/- will get used, quadratics is one of the places where it will be appearing most with little to no absence. We need it for absolute value so we can find which x-values, the positive and negative, will be adequate values for the overall function (and have outputs to the same p-value).
Most other places, however, do not need to use the +/- as a way to find the equation(s) and may only have at most one possible solution, not two.
• how can you solve:
1/2(x-1)^2 +5=23 can we solve it using this method
• Yes... you can.
1) subtract 5 from both sides: 1/2 (x-1)^2 = 18
2) Then multiply both sides by 2 to eliminate the fraction: (x-1)^2 = 36
3) Take square root of both sides: x - 1 = +/- sqrt(36) which simplifies to x - 1 = +/- 6
4) Add 1 to both sides: x = 1 +/- 6
So x = 7 and x = -5
• so what if I have a problem like x=(x -7)2-4 ? (I can't do little two sorry)
(1 vote)
• Anthony, I think that Rhyann97 meant (x-7)^2, since he/she said something about "little two".
x=(x-7)^2-4
=> x=x^2-14x+49-4
=> x^2-15x+45=0
=> Quadratic formula: (15+ - sqrt(225-180))/2
=> (15+ - sqrt(45))/2
=> (15+ - 3sqrt(5))/2.