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Simplifying 171 = 3x + 2x2 Solving 171 = 3x + 2x2 Solving for variable 'x'. Reorder the terms: 171 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 171 + -3x + -2x2 = 0 + 2x2 + -2x2 171 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 171 + -3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -85.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '85.5' to each side of the equation. -85.5 + 1.5x + 85.5 + x2 = 0 + 85.5 Reorder the terms: -85.5 + 85.5 + 1.5x + x2 = 0 + 85.5 Combine like terms: -85.5 + 85.5 = 0.0 0.0 + 1.5x + x2 = 0 + 85.5 1.5x + x2 = 0 + 85.5 Combine like terms: 0 + 85.5 = 85.5 1.5x + x2 = 85.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 85.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 85.5 + 0.5625 Combine like terms: 85.5 + 0.5625 = 86.0625 0.5625 + 1.5x + x2 = 86.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 86.0625 Calculate the square root of the right side: 9.276987658 Break this problem into two subproblems by setting (x + 0.75) equal to 9.276987658 and -9.276987658.Subproblem 1
x + 0.75 = 9.276987658 Simplifying x + 0.75 = 9.276987658 Reorder the terms: 0.75 + x = 9.276987658 Solving 0.75 + x = 9.276987658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 9.276987658 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 9.276987658 + -0.75 x = 9.276987658 + -0.75 Combine like terms: 9.276987658 + -0.75 = 8.526987658 x = 8.526987658 Simplifying x = 8.526987658Subproblem 2
x + 0.75 = -9.276987658 Simplifying x + 0.75 = -9.276987658 Reorder the terms: 0.75 + x = -9.276987658 Solving 0.75 + x = -9.276987658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -9.276987658 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -9.276987658 + -0.75 x = -9.276987658 + -0.75 Combine like terms: -9.276987658 + -0.75 = -10.026987658 x = -10.026987658 Simplifying x = -10.026987658Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.526987658, -10.026987658}
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