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Simplifying 11x + 15x(8x + 5) = 180 Reorder the terms: 11x + 15x(5 + 8x) = 180 11x + (5 * 15x + 8x * 15x) = 180 11x + (75x + 120x2) = 180 Combine like terms: 11x + 75x = 86x 86x + 120x2 = 180 Solving 86x + 120x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 86x + 120x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 86x + 120x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 43x + 60x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 43x + 60x2)' equal to zero and attempt to solve: Simplifying -90 + 43x + 60x2 = 0 Solving -90 + 43x + 60x2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. -1.5 + 0.7166666667x + x2 = 0.0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.7166666667x + 1.5 + x2 = 0.0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.7166666667x + x2 = 0.0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.7166666667x + x2 = 0.0 + 1.5 0.7166666667x + x2 = 0.0 + 1.5 Combine like terms: 0.0 + 1.5 = 1.5 0.7166666667x + x2 = 1.5 The x term is 0.7166666667x. Take half its coefficient (0.3583333334). Square it (0.1284027778) and add it to both sides. Add '0.1284027778' to each side of the equation. 0.7166666667x + 0.1284027778 + x2 = 1.5 + 0.1284027778 Reorder the terms: 0.1284027778 + 0.7166666667x + x2 = 1.5 + 0.1284027778 Combine like terms: 1.5 + 0.1284027778 = 1.6284027778 0.1284027778 + 0.7166666667x + x2 = 1.6284027778 Factor a perfect square on the left side: (x + 0.3583333334)(x + 0.3583333334) = 1.6284027778 Calculate the square root of the right side: 1.27608886 Break this problem into two subproblems by setting (x + 0.3583333334) equal to 1.27608886 and -1.27608886.Subproblem 1
x + 0.3583333334 = 1.27608886 Simplifying x + 0.3583333334 = 1.27608886 Reorder the terms: 0.3583333334 + x = 1.27608886 Solving 0.3583333334 + x = 1.27608886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3583333334' to each side of the equation. 0.3583333334 + -0.3583333334 + x = 1.27608886 + -0.3583333334 Combine like terms: 0.3583333334 + -0.3583333334 = 0.0000000000 0.0000000000 + x = 1.27608886 + -0.3583333334 x = 1.27608886 + -0.3583333334 Combine like terms: 1.27608886 + -0.3583333334 = 0.9177555266 x = 0.9177555266 Simplifying x = 0.9177555266Subproblem 2
x + 0.3583333334 = -1.27608886 Simplifying x + 0.3583333334 = -1.27608886 Reorder the terms: 0.3583333334 + x = -1.27608886 Solving 0.3583333334 + x = -1.27608886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3583333334' to each side of the equation. 0.3583333334 + -0.3583333334 + x = -1.27608886 + -0.3583333334 Combine like terms: 0.3583333334 + -0.3583333334 = 0.0000000000 0.0000000000 + x = -1.27608886 + -0.3583333334 x = -1.27608886 + -0.3583333334 Combine like terms: -1.27608886 + -0.3583333334 = -1.6344221934 x = -1.6344221934 Simplifying x = -1.6344221934Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9177555266, -1.6344221934}Solution
x = {0.9177555266, -1.6344221934}
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