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Simplifying 3x2 + -45x + -87 = 0 Reorder the terms: -87 + -45x + 3x2 = 0 Solving -87 + -45x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-29 + -15x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-29 + -15x + x2)' equal to zero and attempt to solve: Simplifying -29 + -15x + x2 = 0 Solving -29 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -15x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -15x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -15x + x2 = 0 + 29 -15x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -15x + x2 = 29 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 29 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 29 + 56.25 Combine like terms: 29 + 56.25 = 85.25 56.25 + -15x + x2 = 85.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x + -7.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x + -7.5 = 9.233092656 Simplifying x + -7.5 = 9.233092656 Reorder the terms: -7.5 + x = 9.233092656 Solving -7.5 + x = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 9.233092656 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 9.233092656 + 7.5 x = 9.233092656 + 7.5 Combine like terms: 9.233092656 + 7.5 = 16.733092656 x = 16.733092656 Simplifying x = 16.733092656Subproblem 2
x + -7.5 = -9.233092656 Simplifying x + -7.5 = -9.233092656 Reorder the terms: -7.5 + x = -9.233092656 Solving -7.5 + x = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -9.233092656 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -9.233092656 + 7.5 x = -9.233092656 + 7.5 Combine like terms: -9.233092656 + 7.5 = -1.733092656 x = -1.733092656 Simplifying x = -1.733092656Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.733092656, -1.733092656}Solution
x = {16.733092656, -1.733092656}
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