## Find the roots of the following quadratic equation by splitting the middle term x2+20x+99=0​

Question

Find the roots of the following quadratic equation by splitting the
middle term x2+20x+99=0​

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11 months 2021-08-15T06:22:11+00:00 1 Answer 0 views 0

x^2 +20+99 = 0

Simplifying

x2 + -20x + 99 = 0

Reorder the terms:

99 + -20x + x2 = 0

Solving

99 + -20x + x2 = 0

Solving for variable ‘x’.

Factor a trinomial.

(9 + -1x)(11 + -1x) = 0

Subproblem 1

Set the factor ‘(9 + -1x)’ equal to zero and attempt to solve:

Simplifying

9 + -1x = 0

Solving

9 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add ‘-9’ to each side of the equation.

9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0

0 + -1x = 0 + -9

-1x = 0 + -9

Combine like terms: 0 + -9 = -9

-1x = -9

Divide each side by ‘-1’.

x = 9

Simplifying

x = 9

Subproblem 2

Set the factor ‘(11 + -1x)’ equal to zero and attempt to solve:

Simplifying

11 + -1x = 0

Solving

11 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add ‘-11’ to each side of the equation.

11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0

0 + -1x = 0 + -11

-1x = 0 + -11

Combine like terms: 0 + -11 = -11

-1x = -11

Divide each side by ‘-1’.

x = 11

Simplifying

x = 11

Solution

x = {9, 11}