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Simplifying 5(90 + -7x) * x = -126 Reorder the terms for easier multiplication: 5x(90 + -7x) = -126 (90 * 5x + -7x * 5x) = -126 (450x + -35x2) = -126 Solving 450x + -35x2 = -126 Solving for variable 'x'. Reorder the terms: 126 + 450x + -35x2 = -126 + 126 Combine like terms: -126 + 126 = 0 126 + 450x + -35x2 = 0 Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -3.6 + -12.85714286x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -12.85714286x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -12.85714286x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -12.85714286x + x2 = 0 + 3.6 -12.85714286x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -12.85714286x + x2 = 3.6 The x term is -12.85714286x. Take half its coefficient (-6.42857143). Square it (41.32653063) and add it to both sides. Add '41.32653063' to each side of the equation. -12.85714286x + 41.32653063 + x2 = 3.6 + 41.32653063 Reorder the terms: 41.32653063 + -12.85714286x + x2 = 3.6 + 41.32653063 Combine like terms: 3.6 + 41.32653063 = 44.92653063 41.32653063 + -12.85714286x + x2 = 44.92653063 Factor a perfect square on the left side: (x + -6.42857143)(x + -6.42857143) = 44.92653063 Calculate the square root of the right side: 6.702725612 Break this problem into two subproblems by setting (x + -6.42857143) equal to 6.702725612 and -6.702725612.Subproblem 1
x + -6.42857143 = 6.702725612 Simplifying x + -6.42857143 = 6.702725612 Reorder the terms: -6.42857143 + x = 6.702725612 Solving -6.42857143 + x = 6.702725612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + x = 6.702725612 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + x = 6.702725612 + 6.42857143 x = 6.702725612 + 6.42857143 Combine like terms: 6.702725612 + 6.42857143 = 13.131297042 x = 13.131297042 Simplifying x = 13.131297042Subproblem 2
x + -6.42857143 = -6.702725612 Simplifying x + -6.42857143 = -6.702725612 Reorder the terms: -6.42857143 + x = -6.702725612 Solving -6.42857143 + x = -6.702725612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + x = -6.702725612 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + x = -6.702725612 + 6.42857143 x = -6.702725612 + 6.42857143 Combine like terms: -6.702725612 + 6.42857143 = -0.274154182 x = -0.274154182 Simplifying x = -0.274154182Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.131297042, -0.274154182}
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