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Simplifying x2(100 + -1x2) = 2500 (100 * x2 + -1x2 * x2) = 2500 (100x2 + -1x4) = 2500 Solving 100x2 + -1x4 = 2500 Solving for variable 'x'. Reorder the terms: -2500 + 100x2 + -1x4 = 2500 + -2500 Combine like terms: 2500 + -2500 = 0 -2500 + 100x2 + -1x4 = 0 Factor a trinomial. (-50 + x2)(50 + -1x2) = 0Subproblem 1
Set the factor '(-50 + x2)' equal to zero and attempt to solve: Simplifying -50 + x2 = 0 Solving -50 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + x2 = 0 + 50 x2 = 0 + 50 Combine like terms: 0 + 50 = 50 x2 = 50 Simplifying x2 = 50 Take the square root of each side: x = {-7.071067812, 7.071067812}Subproblem 2
Set the factor '(50 + -1x2)' equal to zero and attempt to solve: Simplifying 50 + -1x2 = 0 Solving 50 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1x2 = 0 + -50 -1x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -1x2 = -50 Divide each side by '-1'. x2 = 50 Simplifying x2 = 50 Take the square root of each side: x = {-7.071067812, 7.071067812}Solution
x = {-7.071067812, 7.071067812, -7.071067812, 7.071067812}
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