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Simplifying (x + -4)(x + -5) + (2x + 3)(x + -1) = x(2x + -25 + -13) Reorder the terms: (-4 + x)(x + -5) + (2x + 3)(x + -1) = x(2x + -25 + -13) Reorder the terms: (-4 + x)(-5 + x) + (2x + 3)(x + -1) = x(2x + -25 + -13) Multiply (-4 + x) * (-5 + x) (-4(-5 + x) + x(-5 + x)) + (2x + 3)(x + -1) = x(2x + -25 + -13) ((-5 * -4 + x * -4) + x(-5 + x)) + (2x + 3)(x + -1) = x(2x + -25 + -13) ((20 + -4x) + x(-5 + x)) + (2x + 3)(x + -1) = x(2x + -25 + -13) (20 + -4x + (-5 * x + x * x)) + (2x + 3)(x + -1) = x(2x + -25 + -13) (20 + -4x + (-5x + x2)) + (2x + 3)(x + -1) = x(2x + -25 + -13) Combine like terms: -4x + -5x = -9x (20 + -9x + x2) + (2x + 3)(x + -1) = x(2x + -25 + -13) Reorder the terms: 20 + -9x + x2 + (3 + 2x)(x + -1) = x(2x + -25 + -13) Reorder the terms: 20 + -9x + x2 + (3 + 2x)(-1 + x) = x(2x + -25 + -13) Multiply (3 + 2x) * (-1 + x) 20 + -9x + x2 + (3(-1 + x) + 2x * (-1 + x)) = x(2x + -25 + -13) 20 + -9x + x2 + ((-1 * 3 + x * 3) + 2x * (-1 + x)) = x(2x + -25 + -13) 20 + -9x + x2 + ((-3 + 3x) + 2x * (-1 + x)) = x(2x + -25 + -13) 20 + -9x + x2 + (-3 + 3x + (-1 * 2x + x * 2x)) = x(2x + -25 + -13) 20 + -9x + x2 + (-3 + 3x + (-2x + 2x2)) = x(2x + -25 + -13) Combine like terms: 3x + -2x = 1x 20 + -9x + x2 + (-3 + 1x + 2x2) = x(2x + -25 + -13) Reorder the terms: 20 + -3 + -9x + 1x + x2 + 2x2 = x(2x + -25 + -13) Combine like terms: 20 + -3 = 17 17 + -9x + 1x + x2 + 2x2 = x(2x + -25 + -13) Combine like terms: -9x + 1x = -8x 17 + -8x + x2 + 2x2 = x(2x + -25 + -13) Combine like terms: x2 + 2x2 = 3x2 17 + -8x + 3x2 = x(2x + -25 + -13) Reorder the terms: 17 + -8x + 3x2 = x(-25 + -13 + 2x) Combine like terms: -25 + -13 = -38 17 + -8x + 3x2 = x(-38 + 2x) 17 + -8x + 3x2 = (-38 * x + 2x * x) 17 + -8x + 3x2 = (-38x + 2x2) Solving 17 + -8x + 3x2 = -38x + 2x2 Solving for variable 'x'. Reorder the terms: 17 + -8x + 38x + 3x2 + -2x2 = -38x + 2x2 + 38x + -2x2 Combine like terms: -8x + 38x = 30x 17 + 30x + 3x2 + -2x2 = -38x + 2x2 + 38x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 17 + 30x + 1x2 = -38x + 2x2 + 38x + -2x2 Reorder the terms: 17 + 30x + 1x2 = -38x + 38x + 2x2 + -2x2 Combine like terms: -38x + 38x = 0 17 + 30x + 1x2 = 0 + 2x2 + -2x2 17 + 30x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 17 + 30x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 30x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 30x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 30x + x2 = 0 + -17 30x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 30x + x2 = -17 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -17 + 225 Reorder the terms: 225 + 30x + x2 = -17 + 225 Combine like terms: -17 + 225 = 208 225 + 30x + x2 = 208 Factor a perfect square on the left side: (x + 15)(x + 15) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (x + 15) equal to 14.422205102 and -14.422205102.Subproblem 1
x + 15 = 14.422205102 Simplifying x + 15 = 14.422205102 Reorder the terms: 15 + x = 14.422205102 Solving 15 + x = 14.422205102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 14.422205102 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.422205102 + -15 x = 14.422205102 + -15 Combine like terms: 14.422205102 + -15 = -0.577794898 x = -0.577794898 Simplifying x = -0.577794898Subproblem 2
x + 15 = -14.422205102 Simplifying x + 15 = -14.422205102 Reorder the terms: 15 + x = -14.422205102 Solving 15 + x = -14.422205102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -14.422205102 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.422205102 + -15 x = -14.422205102 + -15 Combine like terms: -14.422205102 + -15 = -29.422205102 x = -29.422205102 Simplifying x = -29.422205102Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.577794898, -29.422205102}
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