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Simplifying 360 = (4x + 10) * 5x + 170 Reorder the terms: 360 = (10 + 4x) * 5x + 170 Reorder the terms for easier multiplication: 360 = 5x(10 + 4x) + 170 360 = (10 * 5x + 4x * 5x) + 170 360 = (50x + 20x2) + 170 Reorder the terms: 360 = 170 + 50x + 20x2 Solving 360 = 170 + 50x + 20x2 Solving for variable 'x'. Combine like terms: 360 + -170 = 190 190 + -50x + -20x2 = 170 + 50x + 20x2 + -170 + -50x + -20x2 Reorder the terms: 190 + -50x + -20x2 = 170 + -170 + 50x + -50x + 20x2 + -20x2 Combine like terms: 170 + -170 = 0 190 + -50x + -20x2 = 0 + 50x + -50x + 20x2 + -20x2 190 + -50x + -20x2 = 50x + -50x + 20x2 + -20x2 Combine like terms: 50x + -50x = 0 190 + -50x + -20x2 = 0 + 20x2 + -20x2 190 + -50x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 190 + -50x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(19 + -5x + -2x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(19 + -5x + -2x2)' equal to zero and attempt to solve: Simplifying 19 + -5x + -2x2 = 0 Solving 19 + -5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -9.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 2.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 2.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 2.5x + x2 = 0 + 9.5 2.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 2.5x + x2 = 9.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 9.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 9.5 + 1.5625 Combine like terms: 9.5 + 1.5625 = 11.0625 1.5625 + 2.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + 1.25) equal to 3.326033674 and -3.326033674.Subproblem 1
x + 1.25 = 3.326033674 Simplifying x + 1.25 = 3.326033674 Reorder the terms: 1.25 + x = 3.326033674 Solving 1.25 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.326033674 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.326033674 + -1.25 x = 3.326033674 + -1.25 Combine like terms: 3.326033674 + -1.25 = 2.076033674 x = 2.076033674 Simplifying x = 2.076033674Subproblem 2
x + 1.25 = -3.326033674 Simplifying x + 1.25 = -3.326033674 Reorder the terms: 1.25 + x = -3.326033674 Solving 1.25 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.326033674 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.326033674 + -1.25 x = -3.326033674 + -1.25 Combine like terms: -3.326033674 + -1.25 = -4.576033674 x = -4.576033674 Simplifying x = -4.576033674Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.076033674, -4.576033674}Solution
x = {2.076033674, -4.576033674}
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