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Simplifying (2x + 5)(3x + -4) = 8 Reorder the terms: (5 + 2x)(3x + -4) = 8 Reorder the terms: (5 + 2x)(-4 + 3x) = 8 Multiply (5 + 2x) * (-4 + 3x) (5(-4 + 3x) + 2x * (-4 + 3x)) = 8 ((-4 * 5 + 3x * 5) + 2x * (-4 + 3x)) = 8 ((-20 + 15x) + 2x * (-4 + 3x)) = 8 (-20 + 15x + (-4 * 2x + 3x * 2x)) = 8 (-20 + 15x + (-8x + 6x2)) = 8 Combine like terms: 15x + -8x = 7x (-20 + 7x + 6x2) = 8 Solving -20 + 7x + 6x2 = 8 Solving for variable 'x'. Reorder the terms: -20 + -8 + 7x + 6x2 = 8 + -8 Combine like terms: -20 + -8 = -28 -28 + 7x + 6x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -28 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.666666667 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + 1.166666667x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + 1.166666667x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + 1.166666667x + x2 = 0 + 4.666666667 1.166666667x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 1.166666667x + x2 = 4.666666667 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = 4.666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 4.666666667 + 0.3402777780 Combine like terms: 4.666666667 + 0.3402777780 = 5.006944445 0.3402777780 + 1.166666667x + x2 = 5.006944445 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 5.006944445 Calculate the square root of the right side: 2.237620264 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 2.237620264 and -2.237620264.Subproblem 1
x + 0.5833333335 = 2.237620264 Simplifying x + 0.5833333335 = 2.237620264 Reorder the terms: 0.5833333335 + x = 2.237620264 Solving 0.5833333335 + x = 2.237620264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 2.237620264 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 2.237620264 + -0.5833333335 x = 2.237620264 + -0.5833333335 Combine like terms: 2.237620264 + -0.5833333335 = 1.6542869305 x = 1.6542869305 Simplifying x = 1.6542869305Subproblem 2
x + 0.5833333335 = -2.237620264 Simplifying x + 0.5833333335 = -2.237620264 Reorder the terms: 0.5833333335 + x = -2.237620264 Solving 0.5833333335 + x = -2.237620264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -2.237620264 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -2.237620264 + -0.5833333335 x = -2.237620264 + -0.5833333335 Combine like terms: -2.237620264 + -0.5833333335 = -2.8209535975 x = -2.8209535975 Simplifying x = -2.8209535975Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6542869305, -2.8209535975}
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