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Simplifying (3x + 7)(x + -8) + -1(x + 4)(x + -2) = 0 Reorder the terms: (7 + 3x)(x + -8) + -1(x + 4)(x + -2) = 0 Reorder the terms: (7 + 3x)(-8 + x) + -1(x + 4)(x + -2) = 0 Multiply (7 + 3x) * (-8 + x) (7(-8 + x) + 3x * (-8 + x)) + -1(x + 4)(x + -2) = 0 ((-8 * 7 + x * 7) + 3x * (-8 + x)) + -1(x + 4)(x + -2) = 0 ((-56 + 7x) + 3x * (-8 + x)) + -1(x + 4)(x + -2) = 0 (-56 + 7x + (-8 * 3x + x * 3x)) + -1(x + 4)(x + -2) = 0 (-56 + 7x + (-24x + 3x2)) + -1(x + 4)(x + -2) = 0 Combine like terms: 7x + -24x = -17x (-56 + -17x + 3x2) + -1(x + 4)(x + -2) = 0 Reorder the terms: -56 + -17x + 3x2 + -1(4 + x)(x + -2) = 0 Reorder the terms: -56 + -17x + 3x2 + -1(4 + x)(-2 + x) = 0 Multiply (4 + x) * (-2 + x) -56 + -17x + 3x2 + -1(4(-2 + x) + x(-2 + x)) = 0 -56 + -17x + 3x2 + -1((-2 * 4 + x * 4) + x(-2 + x)) = 0 -56 + -17x + 3x2 + -1((-8 + 4x) + x(-2 + x)) = 0 -56 + -17x + 3x2 + -1(-8 + 4x + (-2 * x + x * x)) = 0 -56 + -17x + 3x2 + -1(-8 + 4x + (-2x + x2)) = 0 Combine like terms: 4x + -2x = 2x -56 + -17x + 3x2 + -1(-8 + 2x + x2) = 0 -56 + -17x + 3x2 + (-8 * -1 + 2x * -1 + x2 * -1) = 0 -56 + -17x + 3x2 + (8 + -2x + -1x2) = 0 Reorder the terms: -56 + 8 + -17x + -2x + 3x2 + -1x2 = 0 Combine like terms: -56 + 8 = -48 -48 + -17x + -2x + 3x2 + -1x2 = 0 Combine like terms: -17x + -2x = -19x -48 + -19x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 -48 + -19x + 2x2 = 0 Solving -48 + -19x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24 + -9.5x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -9.5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -9.5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -9.5x + x2 = 0 + 24 -9.5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -9.5x + x2 = 24 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 24 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 24 + 22.5625 Combine like terms: 24 + 22.5625 = 46.5625 22.5625 + -9.5x + x2 = 46.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 46.5625 Calculate the square root of the right side: 6.823672032 Break this problem into two subproblems by setting (x + -4.75) equal to 6.823672032 and -6.823672032.Subproblem 1
x + -4.75 = 6.823672032 Simplifying x + -4.75 = 6.823672032 Reorder the terms: -4.75 + x = 6.823672032 Solving -4.75 + x = 6.823672032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 6.823672032 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 6.823672032 + 4.75 x = 6.823672032 + 4.75 Combine like terms: 6.823672032 + 4.75 = 11.573672032 x = 11.573672032 Simplifying x = 11.573672032Subproblem 2
x + -4.75 = -6.823672032 Simplifying x + -4.75 = -6.823672032 Reorder the terms: -4.75 + x = -6.823672032 Solving -4.75 + x = -6.823672032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -6.823672032 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -6.823672032 + 4.75 x = -6.823672032 + 4.75 Combine like terms: -6.823672032 + 4.75 = -2.073672032 x = -2.073672032 Simplifying x = -2.073672032Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.573672032, -2.073672032}
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