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Simplifying (2x + -7)(x + 4) = 33856 Reorder the terms: (-7 + 2x)(x + 4) = 33856 Reorder the terms: (-7 + 2x)(4 + x) = 33856 Multiply (-7 + 2x) * (4 + x) (-7(4 + x) + 2x * (4 + x)) = 33856 ((4 * -7 + x * -7) + 2x * (4 + x)) = 33856 ((-28 + -7x) + 2x * (4 + x)) = 33856 (-28 + -7x + (4 * 2x + x * 2x)) = 33856 (-28 + -7x + (8x + 2x2)) = 33856 Combine like terms: -7x + 8x = 1x (-28 + 1x + 2x2) = 33856 Solving -28 + 1x + 2x2 = 33856 Solving for variable 'x'. Reorder the terms: -28 + -33856 + 1x + 2x2 = 33856 + -33856 Combine like terms: -28 + -33856 = -33884 -33884 + 1x + 2x2 = 33856 + -33856 Combine like terms: 33856 + -33856 = 0 -33884 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16942 + 0.5x + x2 = 0 Move the constant term to the right: Add '16942' to each side of the equation. -16942 + 0.5x + 16942 + x2 = 0 + 16942 Reorder the terms: -16942 + 16942 + 0.5x + x2 = 0 + 16942 Combine like terms: -16942 + 16942 = 0 0 + 0.5x + x2 = 0 + 16942 0.5x + x2 = 0 + 16942 Combine like terms: 0 + 16942 = 16942 0.5x + x2 = 16942 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 16942 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 16942 + 0.0625 Combine like terms: 16942 + 0.0625 = 16942.0625 0.0625 + 0.5x + x2 = 16942.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 16942.0625 Calculate the square root of the right side: 130.161678308 Break this problem into two subproblems by setting (x + 0.25) equal to 130.161678308 and -130.161678308.Subproblem 1
x + 0.25 = 130.161678308 Simplifying x + 0.25 = 130.161678308 Reorder the terms: 0.25 + x = 130.161678308 Solving 0.25 + x = 130.161678308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 130.161678308 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 130.161678308 + -0.25 x = 130.161678308 + -0.25 Combine like terms: 130.161678308 + -0.25 = 129.911678308 x = 129.911678308 Simplifying x = 129.911678308Subproblem 2
x + 0.25 = -130.161678308 Simplifying x + 0.25 = -130.161678308 Reorder the terms: 0.25 + x = -130.161678308 Solving 0.25 + x = -130.161678308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -130.161678308 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -130.161678308 + -0.25 x = -130.161678308 + -0.25 Combine like terms: -130.161678308 + -0.25 = -130.411678308 x = -130.411678308 Simplifying x = -130.411678308Solution
The solution to the problem is based on the solutions from the subproblems. x = {129.911678308, -130.411678308}
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