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Simplifying 11x2 = 8x + 120 Reorder the terms: 11x2 = 120 + 8x Solving 11x2 = 120 + 8x Solving for variable 'x'. Reorder the terms: -120 + -8x + 11x2 = 120 + 8x + -120 + -8x Reorder the terms: -120 + -8x + 11x2 = 120 + -120 + 8x + -8x Combine like terms: 120 + -120 = 0 -120 + -8x + 11x2 = 0 + 8x + -8x -120 + -8x + 11x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -120 + -8x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -10.90909091 + -0.7272727273x + x2 = 0 Move the constant term to the right: Add '10.90909091' to each side of the equation. -10.90909091 + -0.7272727273x + 10.90909091 + x2 = 0 + 10.90909091 Reorder the terms: -10.90909091 + 10.90909091 + -0.7272727273x + x2 = 0 + 10.90909091 Combine like terms: -10.90909091 + 10.90909091 = 0.00000000 0.00000000 + -0.7272727273x + x2 = 0 + 10.90909091 -0.7272727273x + x2 = 0 + 10.90909091 Combine like terms: 0 + 10.90909091 = 10.90909091 -0.7272727273x + x2 = 10.90909091 The x term is -0.7272727273x. Take half its coefficient (-0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. -0.7272727273x + 0.1322314050 + x2 = 10.90909091 + 0.1322314050 Reorder the terms: 0.1322314050 + -0.7272727273x + x2 = 10.90909091 + 0.1322314050 Combine like terms: 10.90909091 + 0.1322314050 = 11.041322315 0.1322314050 + -0.7272727273x + x2 = 11.041322315 Factor a perfect square on the left side: (x + -0.3636363637)(x + -0.3636363637) = 11.041322315 Calculate the square root of the right side: 3.322848524 Break this problem into two subproblems by setting (x + -0.3636363637) equal to 3.322848524 and -3.322848524.Subproblem 1
x + -0.3636363637 = 3.322848524 Simplifying x + -0.3636363637 = 3.322848524 Reorder the terms: -0.3636363637 + x = 3.322848524 Solving -0.3636363637 + x = 3.322848524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = 3.322848524 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = 3.322848524 + 0.3636363637 x = 3.322848524 + 0.3636363637 Combine like terms: 3.322848524 + 0.3636363637 = 3.6864848877 x = 3.6864848877 Simplifying x = 3.6864848877Subproblem 2
x + -0.3636363637 = -3.322848524 Simplifying x + -0.3636363637 = -3.322848524 Reorder the terms: -0.3636363637 + x = -3.322848524 Solving -0.3636363637 + x = -3.322848524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = -3.322848524 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = -3.322848524 + 0.3636363637 x = -3.322848524 + 0.3636363637 Combine like terms: -3.322848524 + 0.3636363637 = -2.9592121603 x = -2.9592121603 Simplifying x = -2.9592121603Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6864848877, -2.9592121603}
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