100+(2x-9)(2x+11)=0

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Solution for 100+(2x-9)(2x+11)=0 equation:


Simplifying
100 + (2x + -9)(2x + 11) = 0

Reorder the terms:
100 + (-9 + 2x)(2x + 11) = 0

Reorder the terms:
100 + (-9 + 2x)(11 + 2x) = 0

Multiply (-9 + 2x) * (11 + 2x)
100 + (-9(11 + 2x) + 2x * (11 + 2x)) = 0
100 + ((11 * -9 + 2x * -9) + 2x * (11 + 2x)) = 0
100 + ((-99 + -18x) + 2x * (11 + 2x)) = 0
100 + (-99 + -18x + (11 * 2x + 2x * 2x)) = 0
100 + (-99 + -18x + (22x + 4x2)) = 0

Combine like terms: -18x + 22x = 4x
100 + (-99 + 4x + 4x2) = 0

Combine like terms: 100 + -99 = 1
1 + 4x + 4x2 = 0

Solving
1 + 4x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + 2x)(1 + 2x) = 0

Subproblem 1

Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5

Subproblem 2

Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5

Solution

x = {-0.5, -0.5}

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