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Simplifying 3x2 + -6x + -87 = 0 Reorder the terms: -87 + -6x + 3x2 = 0 Solving -87 + -6x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-29 + -2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-29 + -2x + x2)' equal to zero and attempt to solve: Simplifying -29 + -2x + x2 = 0 Solving -29 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -2x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -2x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -2x + x2 = 0 + 29 -2x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -2x + x2 = 29 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 29 + 1 Reorder the terms: 1 + -2x + x2 = 29 + 1 Combine like terms: 29 + 1 = 30 1 + -2x + x2 = 30 Factor a perfect square on the left side: (x + -1)(x + -1) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + -1) equal to 5.477225575 and -5.477225575.Subproblem 1
x + -1 = 5.477225575 Simplifying x + -1 = 5.477225575 Reorder the terms: -1 + x = 5.477225575 Solving -1 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.477225575 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.477225575 + 1 x = 5.477225575 + 1 Combine like terms: 5.477225575 + 1 = 6.477225575 x = 6.477225575 Simplifying x = 6.477225575Subproblem 2
x + -1 = -5.477225575 Simplifying x + -1 = -5.477225575 Reorder the terms: -1 + x = -5.477225575 Solving -1 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.477225575 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.477225575 + 1 x = -5.477225575 + 1 Combine like terms: -5.477225575 + 1 = -4.477225575 x = -4.477225575 Simplifying x = -4.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.477225575, -4.477225575}Solution
x = {6.477225575, -4.477225575}
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