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Simplifying 0 = x2 + 15x + -28 Reorder the terms: 0 = -28 + 15x + x2 Solving 0 = -28 + 15x + x2 Solving for variable 'x'. Combine like terms: 0 + 28 = 28 28 + -15x + -1x2 = -28 + 15x + x2 + 28 + -15x + -1x2 Reorder the terms: 28 + -15x + -1x2 = -28 + 28 + 15x + -15x + x2 + -1x2 Combine like terms: -28 + 28 = 0 28 + -15x + -1x2 = 0 + 15x + -15x + x2 + -1x2 28 + -15x + -1x2 = 15x + -15x + x2 + -1x2 Combine like terms: 15x + -15x = 0 28 + -15x + -1x2 = 0 + x2 + -1x2 28 + -15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 28 + -15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + 15x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 15x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 15x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 15x + x2 = 0 + 28 15x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 15x + x2 = 28 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 = 28 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 28 + 56.25 Combine like terms: 28 + 56.25 = 84.25 56.25 + 15x + x2 = 84.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + 7.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + 7.5 = 9.178779875 Simplifying x + 7.5 = 9.178779875 Reorder the terms: 7.5 + x = 9.178779875 Solving 7.5 + x = 9.178779875 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 = 9.178779875 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.178779875 + -7.5 x = 9.178779875 + -7.5 Combine like terms: 9.178779875 + -7.5 = 1.678779875 x = 1.678779875 Simplifying x = 1.678779875Subproblem 2
x + 7.5 = -9.178779875 Simplifying x + 7.5 = -9.178779875 Reorder the terms: 7.5 + x = -9.178779875 Solving 7.5 + x = -9.178779875 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 = -9.178779875 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.178779875 + -7.5 x = -9.178779875 + -7.5 Combine like terms: -9.178779875 + -7.5 = -16.678779875 x = -16.678779875 Simplifying x = -16.678779875Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.678779875, -16.678779875}
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