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Simplifying 80 = (x + 2)(x + 3) Reorder the terms: 80 = (2 + x)(x + 3) Reorder the terms: 80 = (2 + x)(3 + x) Multiply (2 + x) * (3 + x) 80 = (2(3 + x) + x(3 + x)) 80 = ((3 * 2 + x * 2) + x(3 + x)) 80 = ((6 + 2x) + x(3 + x)) 80 = (6 + 2x + (3 * x + x * x)) 80 = (6 + 2x + (3x + x2)) Combine like terms: 2x + 3x = 5x 80 = (6 + 5x + x2) Solving 80 = 6 + 5x + x2 Solving for variable 'x'. Combine like terms: 80 + -6 = 74 74 + -5x + -1x2 = 6 + 5x + x2 + -6 + -5x + -1x2 Reorder the terms: 74 + -5x + -1x2 = 6 + -6 + 5x + -5x + x2 + -1x2 Combine like terms: 6 + -6 = 0 74 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 74 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 74 + -5x + -1x2 = 0 + x2 + -1x2 74 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 74 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -74 + 5x + x2 = 0 Move the constant term to the right: Add '74' to each side of the equation. -74 + 5x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + 5x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + 5x + x2 = 0 + 74 5x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 5x + x2 = 74 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 = 74 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 74 + 6.25 Combine like terms: 74 + 6.25 = 80.25 6.25 + 5x + x2 = 80.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + 2.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + 2.5 = 8.958236434 Simplifying x + 2.5 = 8.958236434 Reorder the terms: 2.5 + x = 8.958236434 Solving 2.5 + x = 8.958236434 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 = 8.958236434 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 8.958236434 + -2.5 x = 8.958236434 + -2.5 Combine like terms: 8.958236434 + -2.5 = 6.458236434 x = 6.458236434 Simplifying x = 6.458236434Subproblem 2
x + 2.5 = -8.958236434 Simplifying x + 2.5 = -8.958236434 Reorder the terms: 2.5 + x = -8.958236434 Solving 2.5 + x = -8.958236434 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 = -8.958236434 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -8.958236434 + -2.5 x = -8.958236434 + -2.5 Combine like terms: -8.958236434 + -2.5 = -11.458236434 x = -11.458236434 Simplifying x = -11.458236434Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.458236434, -11.458236434}
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