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Simplifying (4x + 9)(x) = 360 Reorder the terms: (9 + 4x)(x) = 360 Reorder the terms for easier multiplication: x(9 + 4x) = 360 (9 * x + 4x * x) = 360 (9x + 4x2) = 360 Solving 9x + 4x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 9x + 4x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -90 + 2.25x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 2.25x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 2.25x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 2.25x + x2 = 0 + 90 2.25x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 2.25x + x2 = 90 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 90 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 90 + 1.265625 Combine like terms: 90 + 1.265625 = 91.265625 1.265625 + 2.25x + x2 = 91.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 91.265625 Calculate the square root of the right side: 9.553304402 Break this problem into two subproblems by setting (x + 1.125) equal to 9.553304402 and -9.553304402.Subproblem 1
x + 1.125 = 9.553304402 Simplifying x + 1.125 = 9.553304402 Reorder the terms: 1.125 + x = 9.553304402 Solving 1.125 + x = 9.553304402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 9.553304402 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 9.553304402 + -1.125 x = 9.553304402 + -1.125 Combine like terms: 9.553304402 + -1.125 = 8.428304402 x = 8.428304402 Simplifying x = 8.428304402Subproblem 2
x + 1.125 = -9.553304402 Simplifying x + 1.125 = -9.553304402 Reorder the terms: 1.125 + x = -9.553304402 Solving 1.125 + x = -9.553304402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -9.553304402 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -9.553304402 + -1.125 x = -9.553304402 + -1.125 Combine like terms: -9.553304402 + -1.125 = -10.678304402 x = -10.678304402 Simplifying x = -10.678304402Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.428304402, -10.678304402}
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