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Simplifying 5x2 + 40x + -135 = 0 Reorder the terms: -135 + 40x + 5x2 = 0 Solving -135 + 40x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-27 + 8x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-27 + 8x + x2)' equal to zero and attempt to solve: Simplifying -27 + 8x + x2 = 0 Solving -27 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 8x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 8x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 8x + x2 = 0 + 27 8x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 8x + x2 = 27 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 27 + 16 Reorder the terms: 16 + 8x + x2 = 27 + 16 Combine like terms: 27 + 16 = 43 16 + 8x + x2 = 43 Factor a perfect square on the left side: (x + 4)(x + 4) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + 4) equal to 6.557438524 and -6.557438524.Subproblem 1
x + 4 = 6.557438524 Simplifying x + 4 = 6.557438524 Reorder the terms: 4 + x = 6.557438524 Solving 4 + x = 6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6.557438524 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.557438524 + -4 x = 6.557438524 + -4 Combine like terms: 6.557438524 + -4 = 2.557438524 x = 2.557438524 Simplifying x = 2.557438524Subproblem 2
x + 4 = -6.557438524 Simplifying x + 4 = -6.557438524 Reorder the terms: 4 + x = -6.557438524 Solving 4 + x = -6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6.557438524 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.557438524 + -4 x = -6.557438524 + -4 Combine like terms: -6.557438524 + -4 = -10.557438524 x = -10.557438524 Simplifying x = -10.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.557438524, -10.557438524}Solution
x = {2.557438524, -10.557438524}
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