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Simplifying (4x + 6)(x + -4) = 8 Reorder the terms: (6 + 4x)(x + -4) = 8 Reorder the terms: (6 + 4x)(-4 + x) = 8 Multiply (6 + 4x) * (-4 + x) (6(-4 + x) + 4x * (-4 + x)) = 8 ((-4 * 6 + x * 6) + 4x * (-4 + x)) = 8 ((-24 + 6x) + 4x * (-4 + x)) = 8 (-24 + 6x + (-4 * 4x + x * 4x)) = 8 (-24 + 6x + (-16x + 4x2)) = 8 Combine like terms: 6x + -16x = -10x (-24 + -10x + 4x2) = 8 Solving -24 + -10x + 4x2 = 8 Solving for variable 'x'. Reorder the terms: -24 + -8 + -10x + 4x2 = 8 + -8 Combine like terms: -24 + -8 = -32 -32 + -10x + 4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -32 + -10x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -5x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying -16 + -5x + 2x2 = 0 Solving -16 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + -2.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -2.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -2.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -2.5x + x2 = 0 + 8 -2.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -2.5x + x2 = 8 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 8 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 8 + 1.5625 Combine like terms: 8 + 1.5625 = 9.5625 1.5625 + -2.5x + x2 = 9.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x + -1.25) equal to 3.092329219 and -3.092329219.Subproblem 1
x + -1.25 = 3.092329219 Simplifying x + -1.25 = 3.092329219 Reorder the terms: -1.25 + x = 3.092329219 Solving -1.25 + x = 3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 3.092329219 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.092329219 + 1.25 x = 3.092329219 + 1.25 Combine like terms: 3.092329219 + 1.25 = 4.342329219 x = 4.342329219 Simplifying x = 4.342329219Subproblem 2
x + -1.25 = -3.092329219 Simplifying x + -1.25 = -3.092329219 Reorder the terms: -1.25 + x = -3.092329219 Solving -1.25 + x = -3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -3.092329219 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.092329219 + 1.25 x = -3.092329219 + 1.25 Combine like terms: -3.092329219 + 1.25 = -1.842329219 x = -1.842329219 Simplifying x = -1.842329219Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.342329219, -1.842329219}Solution
x = {4.342329219, -1.842329219}
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