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Simplifying (5x + -8)(4x + 8) = 2 Reorder the terms: (-8 + 5x)(4x + 8) = 2 Reorder the terms: (-8 + 5x)(8 + 4x) = 2 Multiply (-8 + 5x) * (8 + 4x) (-8(8 + 4x) + 5x * (8 + 4x)) = 2 ((8 * -8 + 4x * -8) + 5x * (8 + 4x)) = 2 ((-64 + -32x) + 5x * (8 + 4x)) = 2 (-64 + -32x + (8 * 5x + 4x * 5x)) = 2 (-64 + -32x + (40x + 20x2)) = 2 Combine like terms: -32x + 40x = 8x (-64 + 8x + 20x2) = 2 Solving -64 + 8x + 20x2 = 2 Solving for variable 'x'. Reorder the terms: -64 + -2 + 8x + 20x2 = 2 + -2 Combine like terms: -64 + -2 = -66 -66 + 8x + 20x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -66 + 8x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + 4x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + 4x + 10x2)' equal to zero and attempt to solve: Simplifying -33 + 4x + 10x2 = 0 Solving -33 + 4x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3.3 + 0.4x + x2 = 0.0 Move the constant term to the right: Add '3.3' to each side of the equation. -3.3 + 0.4x + 3.3 + x2 = 0.0 + 3.3 Reorder the terms: -3.3 + 3.3 + 0.4x + x2 = 0.0 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + 0.4x + x2 = 0.0 + 3.3 0.4x + x2 = 0.0 + 3.3 Combine like terms: 0.0 + 3.3 = 3.3 0.4x + x2 = 3.3 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 3.3 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 3.3 + 0.04 Combine like terms: 3.3 + 0.04 = 3.34 0.04 + 0.4x + x2 = 3.34 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 3.34 Calculate the square root of the right side: 1.827566688 Break this problem into two subproblems by setting (x + 0.2) equal to 1.827566688 and -1.827566688.Subproblem 1
x + 0.2 = 1.827566688 Simplifying x + 0.2 = 1.827566688 Reorder the terms: 0.2 + x = 1.827566688 Solving 0.2 + x = 1.827566688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.827566688 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.827566688 + -0.2 x = 1.827566688 + -0.2 Combine like terms: 1.827566688 + -0.2 = 1.627566688 x = 1.627566688 Simplifying x = 1.627566688Subproblem 2
x + 0.2 = -1.827566688 Simplifying x + 0.2 = -1.827566688 Reorder the terms: 0.2 + x = -1.827566688 Solving 0.2 + x = -1.827566688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.827566688 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.827566688 + -0.2 x = -1.827566688 + -0.2 Combine like terms: -1.827566688 + -0.2 = -2.027566688 x = -2.027566688 Simplifying x = -2.027566688Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.627566688, -2.027566688}Solution
x = {1.627566688, -2.027566688}
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