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Simplifying 2x2 + 21x + -117 = 0 Reorder the terms: -117 + 21x + 2x2 = 0 Solving -117 + 21x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -58.5 + 10.5x + x2 = 0 Move the constant term to the right: Add '58.5' to each side of the equation. -58.5 + 10.5x + 58.5 + x2 = 0 + 58.5 Reorder the terms: -58.5 + 58.5 + 10.5x + x2 = 0 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + 10.5x + x2 = 0 + 58.5 10.5x + x2 = 0 + 58.5 Combine like terms: 0 + 58.5 = 58.5 10.5x + x2 = 58.5 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 58.5 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 58.5 + 27.5625 Combine like terms: 58.5 + 27.5625 = 86.0625 27.5625 + 10.5x + x2 = 86.0625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 86.0625 Calculate the square root of the right side: 9.276987658 Break this problem into two subproblems by setting (x + 5.25) equal to 9.276987658 and -9.276987658.Subproblem 1
x + 5.25 = 9.276987658 Simplifying x + 5.25 = 9.276987658 Reorder the terms: 5.25 + x = 9.276987658 Solving 5.25 + x = 9.276987658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 9.276987658 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 9.276987658 + -5.25 x = 9.276987658 + -5.25 Combine like terms: 9.276987658 + -5.25 = 4.026987658 x = 4.026987658 Simplifying x = 4.026987658Subproblem 2
x + 5.25 = -9.276987658 Simplifying x + 5.25 = -9.276987658 Reorder the terms: 5.25 + x = -9.276987658 Solving 5.25 + x = -9.276987658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -9.276987658 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -9.276987658 + -5.25 x = -9.276987658 + -5.25 Combine like terms: -9.276987658 + -5.25 = -14.526987658 x = -14.526987658 Simplifying x = -14.526987658Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.026987658, -14.526987658}
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