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Simplifying 2(4x + 7)(-5x + -8) = -38 Reorder the terms: 2(7 + 4x)(-5x + -8) = -38 Reorder the terms: 2(7 + 4x)(-8 + -5x) = -38 Multiply (7 + 4x) * (-8 + -5x) 2(7(-8 + -5x) + 4x * (-8 + -5x)) = -38 2((-8 * 7 + -5x * 7) + 4x * (-8 + -5x)) = -38 2((-56 + -35x) + 4x * (-8 + -5x)) = -38 2(-56 + -35x + (-8 * 4x + -5x * 4x)) = -38 2(-56 + -35x + (-32x + -20x2)) = -38 Combine like terms: -35x + -32x = -67x 2(-56 + -67x + -20x2) = -38 (-56 * 2 + -67x * 2 + -20x2 * 2) = -38 (-112 + -134x + -40x2) = -38 Solving -112 + -134x + -40x2 = -38 Solving for variable 'x'. Reorder the terms: -112 + 38 + -134x + -40x2 = -38 + 38 Combine like terms: -112 + 38 = -74 -74 + -134x + -40x2 = -38 + 38 Combine like terms: -38 + 38 = 0 -74 + -134x + -40x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(37 + 67x + 20x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(37 + 67x + 20x2)' equal to zero and attempt to solve: Simplifying 37 + 67x + 20x2 = 0 Solving 37 + 67x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1.85 + 3.35x + x2 = 0.0 Move the constant term to the right: Add '-1.85' to each side of the equation. 1.85 + 3.35x + -1.85 + x2 = 0.0 + -1.85 Reorder the terms: 1.85 + -1.85 + 3.35x + x2 = 0.0 + -1.85 Combine like terms: 1.85 + -1.85 = 0.00 0.00 + 3.35x + x2 = 0.0 + -1.85 3.35x + x2 = 0.0 + -1.85 Combine like terms: 0.0 + -1.85 = -1.85 3.35x + x2 = -1.85 The x term is 3.35x. Take half its coefficient (1.675). Square it (2.805625) and add it to both sides. Add '2.805625' to each side of the equation. 3.35x + 2.805625 + x2 = -1.85 + 2.805625 Reorder the terms: 2.805625 + 3.35x + x2 = -1.85 + 2.805625 Combine like terms: -1.85 + 2.805625 = 0.955625 2.805625 + 3.35x + x2 = 0.955625 Factor a perfect square on the left side: (x + 1.675)(x + 1.675) = 0.955625 Calculate the square root of the right side: 0.97756074 Break this problem into two subproblems by setting (x + 1.675) equal to 0.97756074 and -0.97756074.Subproblem 1
x + 1.675 = 0.97756074 Simplifying x + 1.675 = 0.97756074 Reorder the terms: 1.675 + x = 0.97756074 Solving 1.675 + x = 0.97756074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.675' to each side of the equation. 1.675 + -1.675 + x = 0.97756074 + -1.675 Combine like terms: 1.675 + -1.675 = 0.000 0.000 + x = 0.97756074 + -1.675 x = 0.97756074 + -1.675 Combine like terms: 0.97756074 + -1.675 = -0.69743926 x = -0.69743926 Simplifying x = -0.69743926Subproblem 2
x + 1.675 = -0.97756074 Simplifying x + 1.675 = -0.97756074 Reorder the terms: 1.675 + x = -0.97756074 Solving 1.675 + x = -0.97756074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.675' to each side of the equation. 1.675 + -1.675 + x = -0.97756074 + -1.675 Combine like terms: 1.675 + -1.675 = 0.000 0.000 + x = -0.97756074 + -1.675 x = -0.97756074 + -1.675 Combine like terms: -0.97756074 + -1.675 = -2.65256074 x = -2.65256074 Simplifying x = -2.65256074Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.69743926, -2.65256074}Solution
x = {-0.69743926, -2.65256074}
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