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Simplifying 0 = 2x2 + 15x + 15 Reorder the terms: 0 = 15 + 15x + 2x2 Solving 0 = 15 + 15x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + -15x + -2x2 = 15 + 15x + 2x2 + -15 + -15x + -2x2 Reorder the terms: -15 + -15x + -2x2 = 15 + -15 + 15x + -15x + 2x2 + -2x2 Combine like terms: 15 + -15 = 0 -15 + -15x + -2x2 = 0 + 15x + -15x + 2x2 + -2x2 -15 + -15x + -2x2 = 15x + -15x + 2x2 + -2x2 Combine like terms: 15x + -15x = 0 -15 + -15x + -2x2 = 0 + 2x2 + -2x2 -15 + -15x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -15 + -15x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 15x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + 15x + 2x2 = 0 Solving 15 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 7.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 7.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 7.5x + x2 = 0 + -7.5 7.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 7.5x + x2 = -7.5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = -7.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -7.5 + 14.0625 Combine like terms: -7.5 + 14.0625 = 6.5625 14.0625 + 7.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + 3.75) equal to 2.561737691 and -2.561737691.Subproblem 1
x + 3.75 = 2.561737691 Simplifying x + 3.75 = 2.561737691 Reorder the terms: 3.75 + x = 2.561737691 Solving 3.75 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 2.561737691 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 2.561737691 + -3.75 x = 2.561737691 + -3.75 Combine like terms: 2.561737691 + -3.75 = -1.188262309 x = -1.188262309 Simplifying x = -1.188262309Subproblem 2
x + 3.75 = -2.561737691 Simplifying x + 3.75 = -2.561737691 Reorder the terms: 3.75 + x = -2.561737691 Solving 3.75 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -2.561737691 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -2.561737691 + -3.75 x = -2.561737691 + -3.75 Combine like terms: -2.561737691 + -3.75 = -6.311737691 x = -6.311737691 Simplifying x = -6.311737691Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.188262309, -6.311737691}Solution
x = {-1.188262309, -6.311737691}
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