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Simplifying 7(2x + -1) + -12 = -2x(x + 10) Reorder the terms: 7(-1 + 2x) + -12 = -2x(x + 10) (-1 * 7 + 2x * 7) + -12 = -2x(x + 10) (-7 + 14x) + -12 = -2x(x + 10) Reorder the terms: -7 + -12 + 14x = -2x(x + 10) Combine like terms: -7 + -12 = -19 -19 + 14x = -2x(x + 10) Reorder the terms: -19 + 14x = -2x(10 + x) -19 + 14x = (10 * -2x + x * -2x) -19 + 14x = (-20x + -2x2) Solving -19 + 14x = -20x + -2x2 Solving for variable 'x'. Combine like terms: 14x + 20x = 34x -19 + 34x + 2x2 = -20x + -2x2 + 20x + 2x2 Reorder the terms: -19 + 34x + 2x2 = -20x + 20x + -2x2 + 2x2 Combine like terms: -20x + 20x = 0 -19 + 34x + 2x2 = 0 + -2x2 + 2x2 -19 + 34x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -19 + 34x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 17x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 17x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 17x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 17x + x2 = 0 + 9.5 17x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 17x + x2 = 9.5 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 9.5 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 9.5 + 72.25 Combine like terms: 9.5 + 72.25 = 81.75 72.25 + 17x + x2 = 81.75 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 81.75 Calculate the square root of the right side: 9.04157066 Break this problem into two subproblems by setting (x + 8.5) equal to 9.04157066 and -9.04157066.Subproblem 1
x + 8.5 = 9.04157066 Simplifying x + 8.5 = 9.04157066 Reorder the terms: 8.5 + x = 9.04157066 Solving 8.5 + x = 9.04157066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 9.04157066 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 9.04157066 + -8.5 x = 9.04157066 + -8.5 Combine like terms: 9.04157066 + -8.5 = 0.54157066 x = 0.54157066 Simplifying x = 0.54157066Subproblem 2
x + 8.5 = -9.04157066 Simplifying x + 8.5 = -9.04157066 Reorder the terms: 8.5 + x = -9.04157066 Solving 8.5 + x = -9.04157066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -9.04157066 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -9.04157066 + -8.5 x = -9.04157066 + -8.5 Combine like terms: -9.04157066 + -8.5 = -17.54157066 x = -17.54157066 Simplifying x = -17.54157066Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.54157066, -17.54157066}
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