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Simplifying 5(x + -3)(x + 8) = 8 Reorder the terms: 5(-3 + x)(x + 8) = 8 Reorder the terms: 5(-3 + x)(8 + x) = 8 Multiply (-3 + x) * (8 + x) 5(-3(8 + x) + x(8 + x)) = 8 5((8 * -3 + x * -3) + x(8 + x)) = 8 5((-24 + -3x) + x(8 + x)) = 8 5(-24 + -3x + (8 * x + x * x)) = 8 5(-24 + -3x + (8x + x2)) = 8 Combine like terms: -3x + 8x = 5x 5(-24 + 5x + x2) = 8 (-24 * 5 + 5x * 5 + x2 * 5) = 8 (-120 + 25x + 5x2) = 8 Solving -120 + 25x + 5x2 = 8 Solving for variable 'x'. Reorder the terms: -120 + -8 + 25x + 5x2 = 8 + -8 Combine like terms: -120 + -8 = -128 -128 + 25x + 5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -128 + 25x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -25.6 + 5x + x2 = 0 Move the constant term to the right: Add '25.6' to each side of the equation. -25.6 + 5x + 25.6 + x2 = 0 + 25.6 Reorder the terms: -25.6 + 25.6 + 5x + x2 = 0 + 25.6 Combine like terms: -25.6 + 25.6 = 0.0 0.0 + 5x + x2 = 0 + 25.6 5x + x2 = 0 + 25.6 Combine like terms: 0 + 25.6 = 25.6 5x + x2 = 25.6 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 = 25.6 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 25.6 + 6.25 Combine like terms: 25.6 + 6.25 = 31.85 6.25 + 5x + x2 = 31.85 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 31.85 Calculate the square root of the right side: 5.643580424 Break this problem into two subproblems by setting (x + 2.5) equal to 5.643580424 and -5.643580424.Subproblem 1
x + 2.5 = 5.643580424 Simplifying x + 2.5 = 5.643580424 Reorder the terms: 2.5 + x = 5.643580424 Solving 2.5 + x = 5.643580424 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 = 5.643580424 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.643580424 + -2.5 x = 5.643580424 + -2.5 Combine like terms: 5.643580424 + -2.5 = 3.143580424 x = 3.143580424 Simplifying x = 3.143580424Subproblem 2
x + 2.5 = -5.643580424 Simplifying x + 2.5 = -5.643580424 Reorder the terms: 2.5 + x = -5.643580424 Solving 2.5 + x = -5.643580424 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 = -5.643580424 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.643580424 + -2.5 x = -5.643580424 + -2.5 Combine like terms: -5.643580424 + -2.5 = -8.143580424 x = -8.143580424 Simplifying x = -8.143580424Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.143580424, -8.143580424}
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