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Simplifying 2x(4x + 2) + -1(9x + 36) + 18x = 10x + -11 Reorder the terms: 2x(2 + 4x) + -1(9x + 36) + 18x = 10x + -11 (2 * 2x + 4x * 2x) + -1(9x + 36) + 18x = 10x + -11 (4x + 8x2) + -1(9x + 36) + 18x = 10x + -11 Reorder the terms: 4x + 8x2 + -1(36 + 9x) + 18x = 10x + -11 4x + 8x2 + (36 * -1 + 9x * -1) + 18x = 10x + -11 4x + 8x2 + (-36 + -9x) + 18x = 10x + -11 Reorder the terms: -36 + 4x + -9x + 18x + 8x2 = 10x + -11 Combine like terms: 4x + -9x = -5x -36 + -5x + 18x + 8x2 = 10x + -11 Combine like terms: -5x + 18x = 13x -36 + 13x + 8x2 = 10x + -11 Reorder the terms: -36 + 13x + 8x2 = -11 + 10x Solving -36 + 13x + 8x2 = -11 + 10x Solving for variable 'x'. Reorder the terms: -36 + 11 + 13x + -10x + 8x2 = -11 + 10x + 11 + -10x Combine like terms: -36 + 11 = -25 -25 + 13x + -10x + 8x2 = -11 + 10x + 11 + -10x Combine like terms: 13x + -10x = 3x -25 + 3x + 8x2 = -11 + 10x + 11 + -10x Reorder the terms: -25 + 3x + 8x2 = -11 + 11 + 10x + -10x Combine like terms: -11 + 11 = 0 -25 + 3x + 8x2 = 0 + 10x + -10x -25 + 3x + 8x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -25 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + 0.375x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 0.375x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 0.375x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 0.375x + x2 = 0 + 3.125 0.375x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 0.375x + x2 = 3.125 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 3.125 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 3.125 + 0.03515625 Combine like terms: 3.125 + 0.03515625 = 3.16015625 0.03515625 + 0.375x + x2 = 3.16015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 3.16015625 Calculate the square root of the right side: 1.777682832 Break this problem into two subproblems by setting (x + 0.1875) equal to 1.777682832 and -1.777682832.Subproblem 1
x + 0.1875 = 1.777682832 Simplifying x + 0.1875 = 1.777682832 Reorder the terms: 0.1875 + x = 1.777682832 Solving 0.1875 + x = 1.777682832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 1.777682832 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.777682832 + -0.1875 x = 1.777682832 + -0.1875 Combine like terms: 1.777682832 + -0.1875 = 1.590182832 x = 1.590182832 Simplifying x = 1.590182832Subproblem 2
x + 0.1875 = -1.777682832 Simplifying x + 0.1875 = -1.777682832 Reorder the terms: 0.1875 + x = -1.777682832 Solving 0.1875 + x = -1.777682832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -1.777682832 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.777682832 + -0.1875 x = -1.777682832 + -0.1875 Combine like terms: -1.777682832 + -0.1875 = -1.965182832 x = -1.965182832 Simplifying x = -1.965182832Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.590182832, -1.965182832}
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