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Simplifying (x + 8)(2x + -7) = 3 Reorder the terms: (8 + x)(2x + -7) = 3 Reorder the terms: (8 + x)(-7 + 2x) = 3 Multiply (8 + x) * (-7 + 2x) (8(-7 + 2x) + x(-7 + 2x)) = 3 ((-7 * 8 + 2x * 8) + x(-7 + 2x)) = 3 ((-56 + 16x) + x(-7 + 2x)) = 3 (-56 + 16x + (-7 * x + 2x * x)) = 3 (-56 + 16x + (-7x + 2x2)) = 3 Combine like terms: 16x + -7x = 9x (-56 + 9x + 2x2) = 3 Solving -56 + 9x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -56 + -3 + 9x + 2x2 = 3 + -3 Combine like terms: -56 + -3 = -59 -59 + 9x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -59 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -29.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '29.5' to each side of the equation. -29.5 + 4.5x + 29.5 + x2 = 0 + 29.5 Reorder the terms: -29.5 + 29.5 + 4.5x + x2 = 0 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + 4.5x + x2 = 0 + 29.5 4.5x + x2 = 0 + 29.5 Combine like terms: 0 + 29.5 = 29.5 4.5x + x2 = 29.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 29.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 29.5 + 5.0625 Combine like terms: 29.5 + 5.0625 = 34.5625 5.0625 + 4.5x + x2 = 34.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 34.5625 Calculate the square root of the right side: 5.878988008 Break this problem into two subproblems by setting (x + 2.25) equal to 5.878988008 and -5.878988008.Subproblem 1
x + 2.25 = 5.878988008 Simplifying x + 2.25 = 5.878988008 Reorder the terms: 2.25 + x = 5.878988008 Solving 2.25 + x = 5.878988008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 5.878988008 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 5.878988008 + -2.25 x = 5.878988008 + -2.25 Combine like terms: 5.878988008 + -2.25 = 3.628988008 x = 3.628988008 Simplifying x = 3.628988008Subproblem 2
x + 2.25 = -5.878988008 Simplifying x + 2.25 = -5.878988008 Reorder the terms: 2.25 + x = -5.878988008 Solving 2.25 + x = -5.878988008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -5.878988008 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -5.878988008 + -2.25 x = -5.878988008 + -2.25 Combine like terms: -5.878988008 + -2.25 = -8.128988008 x = -8.128988008 Simplifying x = -8.128988008Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.628988008, -8.128988008}
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