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Simplifying (7x + 6)(x + -2) = (6x + -7)(x + -3) Reorder the terms: (6 + 7x)(x + -2) = (6x + -7)(x + -3) Reorder the terms: (6 + 7x)(-2 + x) = (6x + -7)(x + -3) Multiply (6 + 7x) * (-2 + x) (6(-2 + x) + 7x * (-2 + x)) = (6x + -7)(x + -3) ((-2 * 6 + x * 6) + 7x * (-2 + x)) = (6x + -7)(x + -3) ((-12 + 6x) + 7x * (-2 + x)) = (6x + -7)(x + -3) (-12 + 6x + (-2 * 7x + x * 7x)) = (6x + -7)(x + -3) (-12 + 6x + (-14x + 7x2)) = (6x + -7)(x + -3) Combine like terms: 6x + -14x = -8x (-12 + -8x + 7x2) = (6x + -7)(x + -3) Reorder the terms: -12 + -8x + 7x2 = (-7 + 6x)(x + -3) Reorder the terms: -12 + -8x + 7x2 = (-7 + 6x)(-3 + x) Multiply (-7 + 6x) * (-3 + x) -12 + -8x + 7x2 = (-7(-3 + x) + 6x * (-3 + x)) -12 + -8x + 7x2 = ((-3 * -7 + x * -7) + 6x * (-3 + x)) -12 + -8x + 7x2 = ((21 + -7x) + 6x * (-3 + x)) -12 + -8x + 7x2 = (21 + -7x + (-3 * 6x + x * 6x)) -12 + -8x + 7x2 = (21 + -7x + (-18x + 6x2)) Combine like terms: -7x + -18x = -25x -12 + -8x + 7x2 = (21 + -25x + 6x2) Solving -12 + -8x + 7x2 = 21 + -25x + 6x2 Solving for variable 'x'. Reorder the terms: -12 + -21 + -8x + 25x + 7x2 + -6x2 = 21 + -25x + 6x2 + -21 + 25x + -6x2 Combine like terms: -12 + -21 = -33 -33 + -8x + 25x + 7x2 + -6x2 = 21 + -25x + 6x2 + -21 + 25x + -6x2 Combine like terms: -8x + 25x = 17x -33 + 17x + 7x2 + -6x2 = 21 + -25x + 6x2 + -21 + 25x + -6x2 Combine like terms: 7x2 + -6x2 = 1x2 -33 + 17x + 1x2 = 21 + -25x + 6x2 + -21 + 25x + -6x2 Reorder the terms: -33 + 17x + 1x2 = 21 + -21 + -25x + 25x + 6x2 + -6x2 Combine like terms: 21 + -21 = 0 -33 + 17x + 1x2 = 0 + -25x + 25x + 6x2 + -6x2 -33 + 17x + 1x2 = -25x + 25x + 6x2 + -6x2 Combine like terms: -25x + 25x = 0 -33 + 17x + 1x2 = 0 + 6x2 + -6x2 -33 + 17x + 1x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -33 + 17x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 17x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 17x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 17x + x2 = 0 + 33 17x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 17x + x2 = 33 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 33 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 33 + 72.25 Combine like terms: 33 + 72.25 = 105.25 72.25 + 17x + x2 = 105.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 105.25 Calculate the square root of the right side: 10.259142264 Break this problem into two subproblems by setting (x + 8.5) equal to 10.259142264 and -10.259142264.Subproblem 1
x + 8.5 = 10.259142264 Simplifying x + 8.5 = 10.259142264 Reorder the terms: 8.5 + x = 10.259142264 Solving 8.5 + x = 10.259142264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 10.259142264 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 10.259142264 + -8.5 x = 10.259142264 + -8.5 Combine like terms: 10.259142264 + -8.5 = 1.759142264 x = 1.759142264 Simplifying x = 1.759142264Subproblem 2
x + 8.5 = -10.259142264 Simplifying x + 8.5 = -10.259142264 Reorder the terms: 8.5 + x = -10.259142264 Solving 8.5 + x = -10.259142264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -10.259142264 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -10.259142264 + -8.5 x = -10.259142264 + -8.5 Combine like terms: -10.259142264 + -8.5 = -18.759142264 x = -18.759142264 Simplifying x = -18.759142264Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.759142264, -18.759142264}
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