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Simplifying (x + -3) * 2 = (x + 9)(x + -9) Reorder the terms: (-3 + x) * 2 = (x + 9)(x + -9) Reorder the terms for easier multiplication: 2(-3 + x) = (x + 9)(x + -9) (-3 * 2 + x * 2) = (x + 9)(x + -9) (-6 + 2x) = (x + 9)(x + -9) Reorder the terms: -6 + 2x = (9 + x)(x + -9) Reorder the terms: -6 + 2x = (9 + x)(-9 + x) Multiply (9 + x) * (-9 + x) -6 + 2x = (9(-9 + x) + x(-9 + x)) -6 + 2x = ((-9 * 9 + x * 9) + x(-9 + x)) -6 + 2x = ((-81 + 9x) + x(-9 + x)) -6 + 2x = (-81 + 9x + (-9 * x + x * x)) -6 + 2x = (-81 + 9x + (-9x + x2)) Combine like terms: 9x + -9x = 0 -6 + 2x = (-81 + 0 + x2) -6 + 2x = (-81 + x2) Solving -6 + 2x = -81 + x2 Solving for variable 'x'. Reorder the terms: -6 + 81 + 2x + -1x2 = -81 + x2 + 81 + -1x2 Combine like terms: -6 + 81 = 75 75 + 2x + -1x2 = -81 + x2 + 81 + -1x2 Reorder the terms: 75 + 2x + -1x2 = -81 + 81 + x2 + -1x2 Combine like terms: -81 + 81 = 0 75 + 2x + -1x2 = 0 + x2 + -1x2 75 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 75 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -75 + -2x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + -2x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -2x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -2x + x2 = 0 + 75 -2x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -2x + x2 = 75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 75 + 1 Reorder the terms: 1 + -2x + x2 = 75 + 1 Combine like terms: 75 + 1 = 76 1 + -2x + x2 = 76 Factor a perfect square on the left side: (x + -1)(x + -1) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + -1) equal to 8.717797887 and -8.717797887.Subproblem 1
x + -1 = 8.717797887 Simplifying x + -1 = 8.717797887 Reorder the terms: -1 + x = 8.717797887 Solving -1 + x = 8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 8.717797887 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.717797887 + 1 x = 8.717797887 + 1 Combine like terms: 8.717797887 + 1 = 9.717797887 x = 9.717797887 Simplifying x = 9.717797887Subproblem 2
x + -1 = -8.717797887 Simplifying x + -1 = -8.717797887 Reorder the terms: -1 + x = -8.717797887 Solving -1 + x = -8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -8.717797887 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.717797887 + 1 x = -8.717797887 + 1 Combine like terms: -8.717797887 + 1 = -7.717797887 x = -7.717797887 Simplifying x = -7.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.717797887, -7.717797887}
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