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Simplifying 3x2 + -15x + -87 = 0 Reorder the terms: -87 + -15x + 3x2 = 0 Solving -87 + -15x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-29 + -5x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-29 + -5x + x2)' equal to zero and attempt to solve: Simplifying -29 + -5x + x2 = 0 Solving -29 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -5x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -5x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -5x + x2 = 0 + 29 -5x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -5x + x2 = 29 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 29 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 29 + 6.25 Combine like terms: 29 + 6.25 = 35.25 6.25 + -5x + x2 = 35.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + -2.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + -2.5 = 5.937171044 Simplifying x + -2.5 = 5.937171044 Reorder the terms: -2.5 + x = 5.937171044 Solving -2.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 5.937171044 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.937171044 + 2.5 x = 5.937171044 + 2.5 Combine like terms: 5.937171044 + 2.5 = 8.437171044 x = 8.437171044 Simplifying x = 8.437171044Subproblem 2
x + -2.5 = -5.937171044 Simplifying x + -2.5 = -5.937171044 Reorder the terms: -2.5 + x = -5.937171044 Solving -2.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -5.937171044 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.937171044 + 2.5 x = -5.937171044 + 2.5 Combine like terms: -5.937171044 + 2.5 = -3.437171044 x = -3.437171044 Simplifying x = -3.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.437171044, -3.437171044}Solution
x = {8.437171044, -3.437171044}
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