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Simplifying -5x2 + -75x + -156 = 0 Reorder the terms: -156 + -75x + -5x2 = 0 Solving -156 + -75x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(156 + 75x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(156 + 75x + 5x2)' equal to zero and attempt to solve: Simplifying 156 + 75x + 5x2 = 0 Solving 156 + 75x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 31.2 + 15x + x2 = 0 Move the constant term to the right: Add '-31.2' to each side of the equation. 31.2 + 15x + -31.2 + x2 = 0 + -31.2 Reorder the terms: 31.2 + -31.2 + 15x + x2 = 0 + -31.2 Combine like terms: 31.2 + -31.2 = 0.0 0.0 + 15x + x2 = 0 + -31.2 15x + x2 = 0 + -31.2 Combine like terms: 0 + -31.2 = -31.2 15x + x2 = -31.2 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 = -31.2 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -31.2 + 56.25 Combine like terms: -31.2 + 56.25 = 25.05 56.25 + 15x + x2 = 25.05 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 25.05 Calculate the square root of the right side: 5.004997502 Break this problem into two subproblems by setting (x + 7.5) equal to 5.004997502 and -5.004997502.Subproblem 1
x + 7.5 = 5.004997502 Simplifying x + 7.5 = 5.004997502 Reorder the terms: 7.5 + x = 5.004997502 Solving 7.5 + x = 5.004997502 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 = 5.004997502 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 5.004997502 + -7.5 x = 5.004997502 + -7.5 Combine like terms: 5.004997502 + -7.5 = -2.495002498 x = -2.495002498 Simplifying x = -2.495002498Subproblem 2
x + 7.5 = -5.004997502 Simplifying x + 7.5 = -5.004997502 Reorder the terms: 7.5 + x = -5.004997502 Solving 7.5 + x = -5.004997502 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 = -5.004997502 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -5.004997502 + -7.5 x = -5.004997502 + -7.5 Combine like terms: -5.004997502 + -7.5 = -12.504997502 x = -12.504997502 Simplifying x = -12.504997502Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.495002498, -12.504997502}Solution
x = {-2.495002498, -12.504997502}
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