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Simplifying (x + -10)(x + -10) + -1 = 0 Reorder the terms: (-10 + x)(x + -10) + -1 = 0 Reorder the terms: (-10 + x)(-10 + x) + -1 = 0 Multiply (-10 + x) * (-10 + x) (-10(-10 + x) + x(-10 + x)) + -1 = 0 ((-10 * -10 + x * -10) + x(-10 + x)) + -1 = 0 ((100 + -10x) + x(-10 + x)) + -1 = 0 (100 + -10x + (-10 * x + x * x)) + -1 = 0 (100 + -10x + (-10x + x2)) + -1 = 0 Combine like terms: -10x + -10x = -20x (100 + -20x + x2) + -1 = 0 Reorder the terms: 100 + -1 + -20x + x2 = 0 Combine like terms: 100 + -1 = 99 99 + -20x + x2 = 0 Solving 99 + -20x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (9 + -1x)(11 + -1x) = 0Subproblem 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 = 9Subproblem 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 = 11Solution
x = {9, 11}
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