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Simplifying 3x2 + -27x + -87 = 0 Reorder the terms: -87 + -27x + 3x2 = 0 Solving -87 + -27x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-29 + -9x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-29 + -9x + x2)' equal to zero and attempt to solve: Simplifying -29 + -9x + x2 = 0 Solving -29 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -9x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -9x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -9x + x2 = 0 + 29 -9x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -9x + x2 = 29 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 29 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 29 + 20.25 Combine like terms: 29 + 20.25 = 49.25 20.25 + -9x + x2 = 49.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + -4.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + -4.5 = 7.017834424 Simplifying x + -4.5 = 7.017834424 Reorder the terms: -4.5 + x = 7.017834424 Solving -4.5 + x = 7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 7.017834424 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.017834424 + 4.5 x = 7.017834424 + 4.5 Combine like terms: 7.017834424 + 4.5 = 11.517834424 x = 11.517834424 Simplifying x = 11.517834424Subproblem 2
x + -4.5 = -7.017834424 Simplifying x + -4.5 = -7.017834424 Reorder the terms: -4.5 + x = -7.017834424 Solving -4.5 + x = -7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -7.017834424 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.017834424 + 4.5 x = -7.017834424 + 4.5 Combine like terms: -7.017834424 + 4.5 = -2.517834424 x = -2.517834424 Simplifying x = -2.517834424Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.517834424, -2.517834424}Solution
x = {11.517834424, -2.517834424}
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