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Simplifying 0 = x2 + 15x + -178.75 Reorder the terms: 0 = -178.75 + 15x + x2 Solving 0 = -178.75 + 15x + x2 Solving for variable 'x'. Combine like terms: 0 + 178.75 = 178.75 178.75 + -15x + -1x2 = -178.75 + 15x + x2 + 178.75 + -15x + -1x2 Reorder the terms: 178.75 + -15x + -1x2 = -178.75 + 178.75 + 15x + -15x + x2 + -1x2 Combine like terms: -178.75 + 178.75 = 0.00 178.75 + -15x + -1x2 = 0.00 + 15x + -15x + x2 + -1x2 178.75 + -15x + -1x2 = 15x + -15x + x2 + -1x2 Combine like terms: 15x + -15x = 0 178.75 + -15x + -1x2 = 0 + x2 + -1x2 178.75 + -15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 178.75 + -15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -178.75 + 15x + x2 = 0 Move the constant term to the right: Add '178.75' to each side of the equation. -178.75 + 15x + 178.75 + x2 = 0 + 178.75 Reorder the terms: -178.75 + 178.75 + 15x + x2 = 0 + 178.75 Combine like terms: -178.75 + 178.75 = 0.00 0.00 + 15x + x2 = 0 + 178.75 15x + x2 = 0 + 178.75 Combine like terms: 0 + 178.75 = 178.75 15x + x2 = 178.75 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 = 178.75 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 178.75 + 56.25 Combine like terms: 178.75 + 56.25 = 235 56.25 + 15x + x2 = 235 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 235 Calculate the square root of the right side: 15.329709717 Break this problem into two subproblems by setting (x + 7.5) equal to 15.329709717 and -15.329709717.Subproblem 1
x + 7.5 = 15.329709717 Simplifying x + 7.5 = 15.329709717 Reorder the terms: 7.5 + x = 15.329709717 Solving 7.5 + x = 15.329709717 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 = 15.329709717 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 15.329709717 + -7.5 x = 15.329709717 + -7.5 Combine like terms: 15.329709717 + -7.5 = 7.829709717 x = 7.829709717 Simplifying x = 7.829709717Subproblem 2
x + 7.5 = -15.329709717 Simplifying x + 7.5 = -15.329709717 Reorder the terms: 7.5 + x = -15.329709717 Solving 7.5 + x = -15.329709717 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 = -15.329709717 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -15.329709717 + -7.5 x = -15.329709717 + -7.5 Combine like terms: -15.329709717 + -7.5 = -22.829709717 x = -22.829709717 Simplifying x = -22.829709717Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.829709717, -22.829709717}
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