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Simplifying 2x(4 + x) = 117 (4 * 2x + x * 2x) = 117 (8x + 2x2) = 117 Solving 8x + 2x2 = 117 Solving for variable 'x'. Reorder the terms: -117 + 8x + 2x2 = 117 + -117 Combine like terms: 117 + -117 = 0 -117 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -58.5 + 4x + x2 = 0 Move the constant term to the right: Add '58.5' to each side of the equation. -58.5 + 4x + 58.5 + x2 = 0 + 58.5 Reorder the terms: -58.5 + 58.5 + 4x + x2 = 0 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + 4x + x2 = 0 + 58.5 4x + x2 = 0 + 58.5 Combine like terms: 0 + 58.5 = 58.5 4x + x2 = 58.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 58.5 + 4 Reorder the terms: 4 + 4x + x2 = 58.5 + 4 Combine like terms: 58.5 + 4 = 62.5 4 + 4x + x2 = 62.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 62.5 Calculate the square root of the right side: 7.90569415 Break this problem into two subproblems by setting (x + 2) equal to 7.90569415 and -7.90569415.Subproblem 1
x + 2 = 7.90569415 Simplifying x + 2 = 7.90569415 Reorder the terms: 2 + x = 7.90569415 Solving 2 + x = 7.90569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 7.90569415 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.90569415 + -2 x = 7.90569415 + -2 Combine like terms: 7.90569415 + -2 = 5.90569415 x = 5.90569415 Simplifying x = 5.90569415Subproblem 2
x + 2 = -7.90569415 Simplifying x + 2 = -7.90569415 Reorder the terms: 2 + x = -7.90569415 Solving 2 + x = -7.90569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -7.90569415 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.90569415 + -2 x = -7.90569415 + -2 Combine like terms: -7.90569415 + -2 = -9.90569415 x = -9.90569415 Simplifying x = -9.90569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.90569415, -9.90569415}
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