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Simplifying (x + 8)(x + -3) = 119 Reorder the terms: (8 + x)(x + -3) = 119 Reorder the terms: (8 + x)(-3 + x) = 119 Multiply (8 + x) * (-3 + x) (8(-3 + x) + x(-3 + x)) = 119 ((-3 * 8 + x * 8) + x(-3 + x)) = 119 ((-24 + 8x) + x(-3 + x)) = 119 (-24 + 8x + (-3 * x + x * x)) = 119 (-24 + 8x + (-3x + x2)) = 119 Combine like terms: 8x + -3x = 5x (-24 + 5x + x2) = 119 Solving -24 + 5x + x2 = 119 Solving for variable 'x'. Reorder the terms: -24 + -119 + 5x + x2 = 119 + -119 Combine like terms: -24 + -119 = -143 -143 + 5x + x2 = 119 + -119 Combine like terms: 119 + -119 = 0 -143 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '143' to each side of the equation. -143 + 5x + 143 + x2 = 0 + 143 Reorder the terms: -143 + 143 + 5x + x2 = 0 + 143 Combine like terms: -143 + 143 = 0 0 + 5x + x2 = 0 + 143 5x + x2 = 0 + 143 Combine like terms: 0 + 143 = 143 5x + x2 = 143 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 143 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 143 + 6.25 Combine like terms: 143 + 6.25 = 149.25 6.25 + 5x + x2 = 149.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 149.25 Calculate the square root of the right side: 12.216791723 Break this problem into two subproblems by setting (x + 2.5) equal to 12.216791723 and -12.216791723.Subproblem 1
x + 2.5 = 12.216791723 Simplifying x + 2.5 = 12.216791723 Reorder the terms: 2.5 + x = 12.216791723 Solving 2.5 + x = 12.216791723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 12.216791723 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 12.216791723 + -2.5 x = 12.216791723 + -2.5 Combine like terms: 12.216791723 + -2.5 = 9.716791723 x = 9.716791723 Simplifying x = 9.716791723Subproblem 2
x + 2.5 = -12.216791723 Simplifying x + 2.5 = -12.216791723 Reorder the terms: 2.5 + x = -12.216791723 Solving 2.5 + x = -12.216791723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -12.216791723 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -12.216791723 + -2.5 x = -12.216791723 + -2.5 Combine like terms: -12.216791723 + -2.5 = -14.716791723 x = -14.716791723 Simplifying x = -14.716791723Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.716791723, -14.716791723}
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