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Solving Quadratic Equations with Square Roots

Solving Quadratic Equations with Square Roots 1.19 - Solution

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a

Start by isolating 3x23x^2 alone on one side by subtracting 99 from both sides. We can then isolate the x2x^2-term by dividing both sides by 3.3. As the last step, we will square root both sides in order to solve for x.x.

3x2+9=93x^2+9=9
3x2=03x^2=0
x2=0x^2=0
x=±0x=\pm \sqrt{0}
x=0x=0

x=0x=0 solves the equation. Note that x=-0x=\text{-}0 and x=+0x=+0 are equal, and so there is only one solution: x=0.x=0.

b

On the left side, we have two identical terms, i.e. x2.x^2. This means the sum can be written as the product 2x2.2x^2. By dividing both sides by 2,2, you get x2x^2 alone on one side, and can then square root both sides.

x2+x2=200x^2+x^2=200
2x2=2002x^2=200
x2=100x^2=100
x=±100x=\pm\sqrt{100}
x=±10x=\pm 10

Both x=-10x=\text{-}10 and x=10x=10 are solutions to the equation.

c

Start by isolating x2x^2 on one side. Then take the square root of both sides.

2x22=1262x^2-2=126
2x2=1282x^2=128
x2=64x^2=64
x=±64x=\pm \sqrt{64}
x=±8x=\pm 8

Both x=-8x=\text{-}8 and x=8x=8 are solutions to the equation.