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Simplifying 23 + -7(2x + -12) = x + -14 * 5 + (x + -14) * x Reorder the terms: 23 + -7(-12 + 2x) = x + -14 * 5 + (x + -14) * x 23 + (-12 * -7 + 2x * -7) = x + -14 * 5 + (x + -14) * x 23 + (84 + -14x) = x + -14 * 5 + (x + -14) * x Combine like terms: 23 + 84 = 107 107 + -14x = x + -14 * 5 + (x + -14) * x Multiply -14 * 5 107 + -14x = x + -70 + (x + -14) * x Reorder the terms: 107 + -14x = x + -70 + (-14 + x) * x Reorder the terms for easier multiplication: 107 + -14x = x + -70 + x(-14 + x) 107 + -14x = x + -70 + (-14 * x + x * x) 107 + -14x = x + -70 + (-14x + x2) Reorder the terms: 107 + -14x = -70 + x + -14x + x2 Combine like terms: x + -14x = -13x 107 + -14x = -70 + -13x + x2 Solving 107 + -14x = -70 + -13x + x2 Solving for variable 'x'. Reorder the terms: 107 + 70 + -14x + 13x + -1x2 = -70 + -13x + x2 + 70 + 13x + -1x2 Combine like terms: 107 + 70 = 177 177 + -14x + 13x + -1x2 = -70 + -13x + x2 + 70 + 13x + -1x2 Combine like terms: -14x + 13x = -1x 177 + -1x + -1x2 = -70 + -13x + x2 + 70 + 13x + -1x2 Reorder the terms: 177 + -1x + -1x2 = -70 + 70 + -13x + 13x + x2 + -1x2 Combine like terms: -70 + 70 = 0 177 + -1x + -1x2 = 0 + -13x + 13x + x2 + -1x2 177 + -1x + -1x2 = -13x + 13x + x2 + -1x2 Combine like terms: -13x + 13x = 0 177 + -1x + -1x2 = 0 + x2 + -1x2 177 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 177 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -177 + x + x2 = 0 Move the constant term to the right: Add '177' to each side of the equation. -177 + x + 177 + x2 = 0 + 177 Reorder the terms: -177 + 177 + x + x2 = 0 + 177 Combine like terms: -177 + 177 = 0 0 + x + x2 = 0 + 177 x + x2 = 0 + 177 Combine like terms: 0 + 177 = 177 x + x2 = 177 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 177 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 177 + 0.25 Combine like terms: 177 + 0.25 = 177.25 1.25 + x2 = 177.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 177.25 Calculate the square root of the right side: 13.313526956 Break this problem into two subproblems by setting (x + 0.5) equal to 13.313526956 and -13.313526956.Subproblem 1
x + 0.5 = 13.313526956 Simplifying x + 0.5 = 13.313526956 Reorder the terms: 0.5 + x = 13.313526956 Solving 0.5 + x = 13.313526956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 13.313526956 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.313526956 + -0.5 x = 13.313526956 + -0.5 Combine like terms: 13.313526956 + -0.5 = 12.813526956 x = 12.813526956 Simplifying x = 12.813526956Subproblem 2
x + 0.5 = -13.313526956 Simplifying x + 0.5 = -13.313526956 Reorder the terms: 0.5 + x = -13.313526956 Solving 0.5 + x = -13.313526956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -13.313526956 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.313526956 + -0.5 x = -13.313526956 + -0.5 Combine like terms: -13.313526956 + -0.5 = -13.813526956 x = -13.813526956 Simplifying x = -13.813526956Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.813526956, -13.813526956}
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