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Simplifying 80 = (x + 8)(x + 2) Reorder the terms: 80 = (8 + x)(x + 2) Reorder the terms: 80 = (8 + x)(2 + x) Multiply (8 + x) * (2 + x) 80 = (8(2 + x) + x(2 + x)) 80 = ((2 * 8 + x * 8) + x(2 + x)) 80 = ((16 + 8x) + x(2 + x)) 80 = (16 + 8x + (2 * x + x * x)) 80 = (16 + 8x + (2x + x2)) Combine like terms: 8x + 2x = 10x 80 = (16 + 10x + x2) Solving 80 = 16 + 10x + x2 Solving for variable 'x'. Combine like terms: 80 + -16 = 64 64 + -10x + -1x2 = 16 + 10x + x2 + -16 + -10x + -1x2 Reorder the terms: 64 + -10x + -1x2 = 16 + -16 + 10x + -10x + x2 + -1x2 Combine like terms: 16 + -16 = 0 64 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2 64 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 64 + -10x + -1x2 = 0 + x2 + -1x2 64 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 64 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + 10x + x2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 10x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 10x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 10x + x2 = 0 + 64 10x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 10x + x2 = 64 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 64 + 25 Reorder the terms: 25 + 10x + x2 = 64 + 25 Combine like terms: 64 + 25 = 89 25 + 10x + x2 = 89 Factor a perfect square on the left side: (x + 5)(x + 5) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 5) equal to 9.433981132 and -9.433981132.Subproblem 1
x + 5 = 9.433981132 Simplifying x + 5 = 9.433981132 Reorder the terms: 5 + x = 9.433981132 Solving 5 + x = 9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 9.433981132 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.433981132 + -5 x = 9.433981132 + -5 Combine like terms: 9.433981132 + -5 = 4.433981132 x = 4.433981132 Simplifying x = 4.433981132Subproblem 2
x + 5 = -9.433981132 Simplifying x + 5 = -9.433981132 Reorder the terms: 5 + x = -9.433981132 Solving 5 + x = -9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -9.433981132 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.433981132 + -5 x = -9.433981132 + -5 Combine like terms: -9.433981132 + -5 = -14.433981132 x = -14.433981132 Simplifying x = -14.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.433981132, -14.433981132}
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