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Simplifying 2(x + 9)(x + -4) = (x + 7) * x + 84 Reorder the terms: 2(9 + x)(x + -4) = (x + 7) * x + 84 Reorder the terms: 2(9 + x)(-4 + x) = (x + 7) * x + 84 Multiply (9 + x) * (-4 + x) 2(9(-4 + x) + x(-4 + x)) = (x + 7) * x + 84 2((-4 * 9 + x * 9) + x(-4 + x)) = (x + 7) * x + 84 2((-36 + 9x) + x(-4 + x)) = (x + 7) * x + 84 2(-36 + 9x + (-4 * x + x * x)) = (x + 7) * x + 84 2(-36 + 9x + (-4x + x2)) = (x + 7) * x + 84 Combine like terms: 9x + -4x = 5x 2(-36 + 5x + x2) = (x + 7) * x + 84 (-36 * 2 + 5x * 2 + x2 * 2) = (x + 7) * x + 84 (-72 + 10x + 2x2) = (x + 7) * x + 84 Reorder the terms: -72 + 10x + 2x2 = (7 + x) * x + 84 Reorder the terms for easier multiplication: -72 + 10x + 2x2 = x(7 + x) + 84 -72 + 10x + 2x2 = (7 * x + x * x) + 84 -72 + 10x + 2x2 = (7x + x2) + 84 Reorder the terms: -72 + 10x + 2x2 = 84 + 7x + x2 Solving -72 + 10x + 2x2 = 84 + 7x + x2 Solving for variable 'x'. Reorder the terms: -72 + -84 + 10x + -7x + 2x2 + -1x2 = 84 + 7x + x2 + -84 + -7x + -1x2 Combine like terms: -72 + -84 = -156 -156 + 10x + -7x + 2x2 + -1x2 = 84 + 7x + x2 + -84 + -7x + -1x2 Combine like terms: 10x + -7x = 3x -156 + 3x + 2x2 + -1x2 = 84 + 7x + x2 + -84 + -7x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -156 + 3x + 1x2 = 84 + 7x + x2 + -84 + -7x + -1x2 Reorder the terms: -156 + 3x + 1x2 = 84 + -84 + 7x + -7x + x2 + -1x2 Combine like terms: 84 + -84 = 0 -156 + 3x + 1x2 = 0 + 7x + -7x + x2 + -1x2 -156 + 3x + 1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 -156 + 3x + 1x2 = 0 + x2 + -1x2 -156 + 3x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -156 + 3x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '156' to each side of the equation. -156 + 3x + 156 + x2 = 0 + 156 Reorder the terms: -156 + 156 + 3x + x2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + 3x + x2 = 0 + 156 3x + x2 = 0 + 156 Combine like terms: 0 + 156 = 156 3x + x2 = 156 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 156 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 156 + 2.25 Combine like terms: 156 + 2.25 = 158.25 2.25 + 3x + x2 = 158.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 158.25 Calculate the square root of the right side: 12.579745625 Break this problem into two subproblems by setting (x + 1.5) equal to 12.579745625 and -12.579745625.Subproblem 1
x + 1.5 = 12.579745625 Simplifying x + 1.5 = 12.579745625 Reorder the terms: 1.5 + x = 12.579745625 Solving 1.5 + x = 12.579745625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 12.579745625 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.579745625 + -1.5 x = 12.579745625 + -1.5 Combine like terms: 12.579745625 + -1.5 = 11.079745625 x = 11.079745625 Simplifying x = 11.079745625Subproblem 2
x + 1.5 = -12.579745625 Simplifying x + 1.5 = -12.579745625 Reorder the terms: 1.5 + x = -12.579745625 Solving 1.5 + x = -12.579745625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -12.579745625 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.579745625 + -1.5 x = -12.579745625 + -1.5 Combine like terms: -12.579745625 + -1.5 = -14.079745625 x = -14.079745625 Simplifying x = -14.079745625Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.079745625, -14.079745625}
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