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Simplifying 2x(5 + -2x) = -6x(x + 2) + 81 (5 * 2x + -2x * 2x) = -6x(x + 2) + 81 (10x + -4x2) = -6x(x + 2) + 81 Reorder the terms: 10x + -4x2 = -6x(2 + x) + 81 10x + -4x2 = (2 * -6x + x * -6x) + 81 10x + -4x2 = (-12x + -6x2) + 81 Reorder the terms: 10x + -4x2 = 81 + -12x + -6x2 Solving 10x + -4x2 = 81 + -12x + -6x2 Solving for variable 'x'. Reorder the terms: -81 + 10x + 12x + -4x2 + 6x2 = 81 + -12x + -6x2 + -81 + 12x + 6x2 Combine like terms: 10x + 12x = 22x -81 + 22x + -4x2 + 6x2 = 81 + -12x + -6x2 + -81 + 12x + 6x2 Combine like terms: -4x2 + 6x2 = 2x2 -81 + 22x + 2x2 = 81 + -12x + -6x2 + -81 + 12x + 6x2 Reorder the terms: -81 + 22x + 2x2 = 81 + -81 + -12x + 12x + -6x2 + 6x2 Combine like terms: 81 + -81 = 0 -81 + 22x + 2x2 = 0 + -12x + 12x + -6x2 + 6x2 -81 + 22x + 2x2 = -12x + 12x + -6x2 + 6x2 Combine like terms: -12x + 12x = 0 -81 + 22x + 2x2 = 0 + -6x2 + 6x2 -81 + 22x + 2x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -81 + 22x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -40.5 + 11x + x2 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + 11x + 40.5 + x2 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + 11x + x2 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + 11x + x2 = 0 + 40.5 11x + x2 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 11x + x2 = 40.5 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 40.5 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 40.5 + 30.25 Combine like terms: 40.5 + 30.25 = 70.75 30.25 + 11x + x2 = 70.75 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 70.75 Calculate the square root of the right side: 8.411301921 Break this problem into two subproblems by setting (x + 5.5) equal to 8.411301921 and -8.411301921.Subproblem 1
x + 5.5 = 8.411301921 Simplifying x + 5.5 = 8.411301921 Reorder the terms: 5.5 + x = 8.411301921 Solving 5.5 + x = 8.411301921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 8.411301921 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 8.411301921 + -5.5 x = 8.411301921 + -5.5 Combine like terms: 8.411301921 + -5.5 = 2.911301921 x = 2.911301921 Simplifying x = 2.911301921Subproblem 2
x + 5.5 = -8.411301921 Simplifying x + 5.5 = -8.411301921 Reorder the terms: 5.5 + x = -8.411301921 Solving 5.5 + x = -8.411301921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -8.411301921 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -8.411301921 + -5.5 x = -8.411301921 + -5.5 Combine like terms: -8.411301921 + -5.5 = -13.911301921 x = -13.911301921 Simplifying x = -13.911301921Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.911301921, -13.911301921}
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