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Simplifying 8x2 + 17x + -176 = 0 Reorder the terms: -176 + 17x + 8x2 = 0 Solving -176 + 17x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -22 + 2.125x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 2.125x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 2.125x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 2.125x + x2 = 0 + 22 2.125x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 2.125x + x2 = 22 The x term is 2.125x. Take half its coefficient (1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. 2.125x + 1.12890625 + x2 = 22 + 1.12890625 Reorder the terms: 1.12890625 + 2.125x + x2 = 22 + 1.12890625 Combine like terms: 22 + 1.12890625 = 23.12890625 1.12890625 + 2.125x + x2 = 23.12890625 Factor a perfect square on the left side: (x + 1.0625)(x + 1.0625) = 23.12890625 Calculate the square root of the right side: 4.809252151 Break this problem into two subproblems by setting (x + 1.0625) equal to 4.809252151 and -4.809252151.Subproblem 1
x + 1.0625 = 4.809252151 Simplifying x + 1.0625 = 4.809252151 Reorder the terms: 1.0625 + x = 4.809252151 Solving 1.0625 + x = 4.809252151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = 4.809252151 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = 4.809252151 + -1.0625 x = 4.809252151 + -1.0625 Combine like terms: 4.809252151 + -1.0625 = 3.746752151 x = 3.746752151 Simplifying x = 3.746752151Subproblem 2
x + 1.0625 = -4.809252151 Simplifying x + 1.0625 = -4.809252151 Reorder the terms: 1.0625 + x = -4.809252151 Solving 1.0625 + x = -4.809252151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = -4.809252151 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = -4.809252151 + -1.0625 x = -4.809252151 + -1.0625 Combine like terms: -4.809252151 + -1.0625 = -5.871752151 x = -5.871752151 Simplifying x = -5.871752151Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.746752151, -5.871752151}
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