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Simplifying (x + 10)(x + 10)(x + -10)(x + -10) = 0 Reorder the terms: (10 + x)(x + 10)(x + -10)(x + -10) = 0 Reorder the terms: (10 + x)(10 + x)(x + -10)(x + -10) = 0 Reorder the terms: (10 + x)(10 + x)(-10 + x)(x + -10) = 0 Reorder the terms: (10 + x)(10 + x)(-10 + x)(-10 + x) = 0 Multiply (10 + x) * (10 + x) (10(10 + x) + x(10 + x))(-10 + x)(-10 + x) = 0 ((10 * 10 + x * 10) + x(10 + x))(-10 + x)(-10 + x) = 0 ((100 + 10x) + x(10 + x))(-10 + x)(-10 + x) = 0 (100 + 10x + (10 * x + x * x))(-10 + x)(-10 + x) = 0 (100 + 10x + (10x + x2))(-10 + x)(-10 + x) = 0 Combine like terms: 10x + 10x = 20x (100 + 20x + x2)(-10 + x)(-10 + x) = 0 Multiply (100 + 20x + x2) * (-10 + x) (100(-10 + x) + 20x * (-10 + x) + x2(-10 + x))(-10 + x) = 0 ((-10 * 100 + x * 100) + 20x * (-10 + x) + x2(-10 + x))(-10 + x) = 0 ((-1000 + 100x) + 20x * (-10 + x) + x2(-10 + x))(-10 + x) = 0 (-1000 + 100x + (-10 * 20x + x * 20x) + x2(-10 + x))(-10 + x) = 0 (-1000 + 100x + (-200x + 20x2) + x2(-10 + x))(-10 + x) = 0 (-1000 + 100x + -200x + 20x2 + (-10 * x2 + x * x2))(-10 + x) = 0 (-1000 + 100x + -200x + 20x2 + (-10x2 + x3))(-10 + x) = 0 Combine like terms: 100x + -200x = -100x (-1000 + -100x + 20x2 + -10x2 + x3)(-10 + x) = 0 Combine like terms: 20x2 + -10x2 = 10x2 (-1000 + -100x + 10x2 + x3)(-10 + x) = 0 Multiply (-1000 + -100x + 10x2 + x3) * (-10 + x) (-1000(-10 + x) + -100x * (-10 + x) + 10x2 * (-10 + x) + x3(-10 + x)) = 0 ((-10 * -1000 + x * -1000) + -100x * (-10 + x) + 10x2 * (-10 + x) + x3(-10 + x)) = 0 ((10000 + -1000x) + -100x * (-10 + x) + 10x2 * (-10 + x) + x3(-10 + x)) = 0 (10000 + -1000x + (-10 * -100x + x * -100x) + 10x2 * (-10 + x) + x3(-10 + x)) = 0 (10000 + -1000x + (1000x + -100x2) + 10x2 * (-10 + x) + x3(-10 + x)) = 0 (10000 + -1000x + 1000x + -100x2 + (-10 * 10x2 + x * 10x2) + x3(-10 + x)) = 0 (10000 + -1000x + 1000x + -100x2 + (-100x2 + 10x3) + x3(-10 + x)) = 0 (10000 + -1000x + 1000x + -100x2 + -100x2 + 10x3 + (-10 * x3 + x * x3)) = 0 (10000 + -1000x + 1000x + -100x2 + -100x2 + 10x3 + (-10x3 + x4)) = 0 Combine like terms: -1000x + 1000x = 0 (10000 + 0 + -100x2 + -100x2 + 10x3 + -10x3 + x4) = 0 (10000 + -100x2 + -100x2 + 10x3 + -10x3 + x4) = 0 Combine like terms: -100x2 + -100x2 = -200x2 (10000 + -200x2 + 10x3 + -10x3 + x4) = 0 Combine like terms: 10x3 + -10x3 = 0 (10000 + -200x2 + 0 + x4) = 0 (10000 + -200x2 + x4) = 0 Solving 10000 + -200x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (100 + -1x2)(100 + -1x2) = 0 Factor a difference between two squares. ((10 + x)(10 + -1x))(100 + -1x2) = 0 Factor a difference between two squares. ((10 + x)(10 + -1x))(10 + x)(10 + -1x) = 0Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 3
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Subproblem 4
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-10, 10, -10, 10}
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