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Simplifying 60x2 + 87x + -15 = 0 Reorder the terms: -15 + 87x + 60x2 = 0 Solving -15 + 87x + 60x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 29x + 20x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 29x + 20x2)' equal to zero and attempt to solve: Simplifying -5 + 29x + 20x2 = 0 Solving -5 + 29x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.25 + 1.45x + x2 = 0.0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 1.45x + 0.25 + x2 = 0.0 + 0.25 Reorder the terms: -0.25 + 0.25 + 1.45x + x2 = 0.0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 1.45x + x2 = 0.0 + 0.25 1.45x + x2 = 0.0 + 0.25 Combine like terms: 0.0 + 0.25 = 0.25 1.45x + x2 = 0.25 The x term is 1.45x. Take half its coefficient (0.725). Square it (0.525625) and add it to both sides. Add '0.525625' to each side of the equation. 1.45x + 0.525625 + x2 = 0.25 + 0.525625 Reorder the terms: 0.525625 + 1.45x + x2 = 0.25 + 0.525625 Combine like terms: 0.25 + 0.525625 = 0.775625 0.525625 + 1.45x + x2 = 0.775625 Factor a perfect square on the left side: (x + 0.725)(x + 0.725) = 0.775625 Calculate the square root of the right side: 0.880695748 Break this problem into two subproblems by setting (x + 0.725) equal to 0.880695748 and -0.880695748.Subproblem 1
x + 0.725 = 0.880695748 Simplifying x + 0.725 = 0.880695748 Reorder the terms: 0.725 + x = 0.880695748 Solving 0.725 + x = 0.880695748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.725' to each side of the equation. 0.725 + -0.725 + x = 0.880695748 + -0.725 Combine like terms: 0.725 + -0.725 = 0.000 0.000 + x = 0.880695748 + -0.725 x = 0.880695748 + -0.725 Combine like terms: 0.880695748 + -0.725 = 0.155695748 x = 0.155695748 Simplifying x = 0.155695748Subproblem 2
x + 0.725 = -0.880695748 Simplifying x + 0.725 = -0.880695748 Reorder the terms: 0.725 + x = -0.880695748 Solving 0.725 + x = -0.880695748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.725' to each side of the equation. 0.725 + -0.725 + x = -0.880695748 + -0.725 Combine like terms: 0.725 + -0.725 = 0.000 0.000 + x = -0.880695748 + -0.725 x = -0.880695748 + -0.725 Combine like terms: -0.880695748 + -0.725 = -1.605695748 x = -1.605695748 Simplifying x = -1.605695748Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.155695748, -1.605695748}Solution
x = {0.155695748, -1.605695748}
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