Math

QuestionRewrite the equation x2+2x99=0x^{2}+2x-99=0 by completing the square and solve for xx.

Studdy Solution

STEP 1

Assumptions1. The given equation is x+x99=0x^{}+ x-99=0 . We are to rewrite this equation in the form (x+)=(x+)^{}= using the process of completing the square3. We are to solve the equation for xx

STEP 2

The general form of a quadratic equation is ax2+bx+c=0ax^{2} + bx + c =0. In our case, a=1a =1, b=2b =2, and c=99c = -99.

STEP 3

To complete the square, we need to make the left side of the equation a perfect square trinomial. This can be done by adding the square of half of the coefficient of xx to both sides of the equation.

STEP 4

Calculate half of the coefficient of xx, which is b/2ab/2a.
b2a=22×1=1\frac{b}{2a} = \frac{2}{2 \times1} =1

STEP 5

Square the result from the previous step.
(b2a)2=12=1(\frac{b}{2a})^{2} =1^{2} =1

STEP 6

Add the square of half of the coefficient of xx to both sides of the equation.
x2+2x+1=99+1x^{2}+2 x +1 =99 +1

STEP 7

implify the equation.
(x+1)2=100(x+1)^{2} =100So, =1 =1 and =100 =100.

STEP 8

Now, to solve the equation, we take the square root of both sides. Remember that there are two possible solutions, one positive and one negative.
x+1=±100x+1 = \pm \sqrt{100}

STEP 9

implify the equation.
x+=±x+ = \pm

STEP 10

Subtract from both sides to solve for xx.
x=±10x = - \pm10

STEP 11

Calculate the two possible solutions for xx.
x=+10=9x = - +10 =9andx=10=11x = - -10 = -11So, the solutions to the equation are x=9x =9 and x=11x = -11.

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