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Simplifying (x + -2)(x + 5) + -1(x + -7)(x + 1) = (x + 2)(x + -3) Reorder the terms: (-2 + x)(x + 5) + -1(x + -7)(x + 1) = (x + 2)(x + -3) Reorder the terms: (-2 + x)(5 + x) + -1(x + -7)(x + 1) = (x + 2)(x + -3) Multiply (-2 + x) * (5 + x) (-2(5 + x) + x(5 + x)) + -1(x + -7)(x + 1) = (x + 2)(x + -3) ((5 * -2 + x * -2) + x(5 + x)) + -1(x + -7)(x + 1) = (x + 2)(x + -3) ((-10 + -2x) + x(5 + x)) + -1(x + -7)(x + 1) = (x + 2)(x + -3) (-10 + -2x + (5 * x + x * x)) + -1(x + -7)(x + 1) = (x + 2)(x + -3) (-10 + -2x + (5x + x2)) + -1(x + -7)(x + 1) = (x + 2)(x + -3) Combine like terms: -2x + 5x = 3x (-10 + 3x + x2) + -1(x + -7)(x + 1) = (x + 2)(x + -3) Reorder the terms: -10 + 3x + x2 + -1(-7 + x)(x + 1) = (x + 2)(x + -3) Reorder the terms: -10 + 3x + x2 + -1(-7 + x)(1 + x) = (x + 2)(x + -3) Multiply (-7 + x) * (1 + x) -10 + 3x + x2 + -1(-7(1 + x) + x(1 + x)) = (x + 2)(x + -3) -10 + 3x + x2 + -1((1 * -7 + x * -7) + x(1 + x)) = (x + 2)(x + -3) -10 + 3x + x2 + -1((-7 + -7x) + x(1 + x)) = (x + 2)(x + -3) -10 + 3x + x2 + -1(-7 + -7x + (1 * x + x * x)) = (x + 2)(x + -3) -10 + 3x + x2 + -1(-7 + -7x + (1x + x2)) = (x + 2)(x + -3) Combine like terms: -7x + 1x = -6x -10 + 3x + x2 + -1(-7 + -6x + x2) = (x + 2)(x + -3) -10 + 3x + x2 + (-7 * -1 + -6x * -1 + x2 * -1) = (x + 2)(x + -3) -10 + 3x + x2 + (7 + 6x + -1x2) = (x + 2)(x + -3) Reorder the terms: -10 + 7 + 3x + 6x + x2 + -1x2 = (x + 2)(x + -3) Combine like terms: -10 + 7 = -3 -3 + 3x + 6x + x2 + -1x2 = (x + 2)(x + -3) Combine like terms: 3x + 6x = 9x -3 + 9x + x2 + -1x2 = (x + 2)(x + -3) Combine like terms: x2 + -1x2 = 0 -3 + 9x + 0 = (x + 2)(x + -3) -3 + 9x = (x + 2)(x + -3) Reorder the terms: -3 + 9x = (2 + x)(x + -3) Reorder the terms: -3 + 9x = (2 + x)(-3 + x) Multiply (2 + x) * (-3 + x) -3 + 9x = (2(-3 + x) + x(-3 + x)) -3 + 9x = ((-3 * 2 + x * 2) + x(-3 + x)) -3 + 9x = ((-6 + 2x) + x(-3 + x)) -3 + 9x = (-6 + 2x + (-3 * x + x * x)) -3 + 9x = (-6 + 2x + (-3x + x2)) Combine like terms: 2x + -3x = -1x -3 + 9x = (-6 + -1x + x2) Solving -3 + 9x = -6 + -1x + x2 Solving for variable 'x'. Reorder the terms: -3 + 6 + 9x + x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2 Combine like terms: -3 + 6 = 3 3 + 9x + x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2 Combine like terms: 9x + x = 10x 3 + 10x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2 Reorder the terms: 3 + 10x + -1x2 = -6 + 6 + -1x + x + x2 + -1x2 Combine like terms: -6 + 6 = 0 3 + 10x + -1x2 = 0 + -1x + x + x2 + -1x2 3 + 10x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 3 + 10x + -1x2 = 0 + x2 + -1x2 3 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -10x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -10x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -10x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -10x + x2 = 0 + 3 -10x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -10x + x2 = 3 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 3 + 25 Reorder the terms: 25 + -10x + x2 = 3 + 25 Combine like terms: 3 + 25 = 28 25 + -10x + x2 = 28 Factor a perfect square on the left side: (x + -5)(x + -5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -5) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -5 = 5.291502622 Simplifying x + -5 = 5.291502622 Reorder the terms: -5 + x = 5.291502622 Solving -5 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.291502622 + 5 x = 5.291502622 + 5 Combine like terms: 5.291502622 + 5 = 10.291502622 x = 10.291502622 Simplifying x = 10.291502622Subproblem 2
x + -5 = -5.291502622 Simplifying x + -5 = -5.291502622 Reorder the terms: -5 + x = -5.291502622 Solving -5 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.291502622 + 5 x = -5.291502622 + 5 Combine like terms: -5.291502622 + 5 = -0.291502622 x = -0.291502622 Simplifying x = -0.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.291502622, -0.291502622}
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