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Simplifying x(x + -8) = 160 Reorder the terms: x(-8 + x) = 160 (-8 * x + x * x) = 160 (-8x + x2) = 160 Solving -8x + x2 = 160 Solving for variable 'x'. Reorder the terms: -160 + -8x + x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + -8x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -8x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -8x + x2 = 0 + 160 -8x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -8x + x2 = 160 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 160 + 16 Reorder the terms: 16 + -8x + x2 = 160 + 16 Combine like terms: 160 + 16 = 176 16 + -8x + x2 = 176 Factor a perfect square on the left side: (x + -4)(x + -4) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (x + -4) equal to 13.266499161 and -13.266499161.Subproblem 1
x + -4 = 13.266499161 Simplifying x + -4 = 13.266499161 Reorder the terms: -4 + x = 13.266499161 Solving -4 + x = 13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 13.266499161 + 4 Combine like terms: -4 + 4 = 0 0 + x = 13.266499161 + 4 x = 13.266499161 + 4 Combine like terms: 13.266499161 + 4 = 17.266499161 x = 17.266499161 Simplifying x = 17.266499161Subproblem 2
x + -4 = -13.266499161 Simplifying x + -4 = -13.266499161 Reorder the terms: -4 + x = -13.266499161 Solving -4 + x = -13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -13.266499161 + 4 Combine like terms: -4 + 4 = 0 0 + x = -13.266499161 + 4 x = -13.266499161 + 4 Combine like terms: -13.266499161 + 4 = -9.266499161 x = -9.266499161 Simplifying x = -9.266499161Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.266499161, -9.266499161}
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