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Simplifying 0 = x2 + 3x + -82 Reorder the terms: 0 = -82 + 3x + x2 Solving 0 = -82 + 3x + x2 Solving for variable 'x'. Combine like terms: 0 + 82 = 82 82 + -3x + -1x2 = -82 + 3x + x2 + 82 + -3x + -1x2 Reorder the terms: 82 + -3x + -1x2 = -82 + 82 + 3x + -3x + x2 + -1x2 Combine like terms: -82 + 82 = 0 82 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2 82 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 82 + -3x + -1x2 = 0 + x2 + -1x2 82 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 82 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -82 + 3x + x2 = 0 Move the constant term to the right: Add '82' to each side of the equation. -82 + 3x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + 3x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + 3x + x2 = 0 + 82 3x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 3x + x2 = 82 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 82 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 82 + 2.25 Combine like terms: 82 + 2.25 = 84.25 2.25 + 3x + x2 = 84.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + 1.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + 1.5 = 9.178779875 Simplifying x + 1.5 = 9.178779875 Reorder the terms: 1.5 + x = 9.178779875 Solving 1.5 + x = 9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.178779875 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.178779875 + -1.5 x = 9.178779875 + -1.5 Combine like terms: 9.178779875 + -1.5 = 7.678779875 x = 7.678779875 Simplifying x = 7.678779875Subproblem 2
x + 1.5 = -9.178779875 Simplifying x + 1.5 = -9.178779875 Reorder the terms: 1.5 + x = -9.178779875 Solving 1.5 + x = -9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.178779875 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.178779875 + -1.5 x = -9.178779875 + -1.5 Combine like terms: -9.178779875 + -1.5 = -10.678779875 x = -10.678779875 Simplifying x = -10.678779875Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.678779875, -10.678779875}
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