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Simplifying 15.25 = x2 + 10.95x + 27.65 Reorder the terms: 15.25 = 27.65 + 10.95x + x2 Solving 15.25 = 27.65 + 10.95x + x2 Solving for variable 'x'. Combine like terms: 15.25 + -27.65 = -12.4 -12.4 + -10.95x + -1x2 = 27.65 + 10.95x + x2 + -27.65 + -10.95x + -1x2 Reorder the terms: -12.4 + -10.95x + -1x2 = 27.65 + -27.65 + 10.95x + -10.95x + x2 + -1x2 Combine like terms: 27.65 + -27.65 = 0.00 -12.4 + -10.95x + -1x2 = 0.00 + 10.95x + -10.95x + x2 + -1x2 -12.4 + -10.95x + -1x2 = 10.95x + -10.95x + x2 + -1x2 Combine like terms: 10.95x + -10.95x = 0.00 -12.4 + -10.95x + -1x2 = 0.00 + x2 + -1x2 -12.4 + -10.95x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12.4 + -10.95x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12.4 + 10.95x + x2 = 0 Move the constant term to the right: Add '-12.4' to each side of the equation. 12.4 + 10.95x + -12.4 + x2 = 0 + -12.4 Reorder the terms: 12.4 + -12.4 + 10.95x + x2 = 0 + -12.4 Combine like terms: 12.4 + -12.4 = 0.0 0.0 + 10.95x + x2 = 0 + -12.4 10.95x + x2 = 0 + -12.4 Combine like terms: 0 + -12.4 = -12.4 10.95x + x2 = -12.4 The x term is 10.95x. Take half its coefficient (5.475). Square it (29.975625) and add it to both sides. Add '29.975625' to each side of the equation. 10.95x + 29.975625 + x2 = -12.4 + 29.975625 Reorder the terms: 29.975625 + 10.95x + x2 = -12.4 + 29.975625 Combine like terms: -12.4 + 29.975625 = 17.575625 29.975625 + 10.95x + x2 = 17.575625 Factor a perfect square on the left side: (x + 5.475)(x + 5.475) = 17.575625 Calculate the square root of the right side: 4.192329305 Break this problem into two subproblems by setting (x + 5.475) equal to 4.192329305 and -4.192329305.Subproblem 1
x + 5.475 = 4.192329305 Simplifying x + 5.475 = 4.192329305 Reorder the terms: 5.475 + x = 4.192329305 Solving 5.475 + x = 4.192329305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.475' to each side of the equation. 5.475 + -5.475 + x = 4.192329305 + -5.475 Combine like terms: 5.475 + -5.475 = 0.000 0.000 + x = 4.192329305 + -5.475 x = 4.192329305 + -5.475 Combine like terms: 4.192329305 + -5.475 = -1.282670695 x = -1.282670695 Simplifying x = -1.282670695Subproblem 2
x + 5.475 = -4.192329305 Simplifying x + 5.475 = -4.192329305 Reorder the terms: 5.475 + x = -4.192329305 Solving 5.475 + x = -4.192329305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.475' to each side of the equation. 5.475 + -5.475 + x = -4.192329305 + -5.475 Combine like terms: 5.475 + -5.475 = 0.000 0.000 + x = -4.192329305 + -5.475 x = -4.192329305 + -5.475 Combine like terms: -4.192329305 + -5.475 = -9.667329305 x = -9.667329305 Simplifying x = -9.667329305Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.282670695, -9.667329305}
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