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Simplifying 8x2 + 32x + -17 = 0 Reorder the terms: -17 + 32x + 8x2 = 0 Solving -17 + 32x + 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'. -2.125 + 4x + x2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + 4x + 2.125 + x2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + 4x + x2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + 4x + x2 = 0 + 2.125 4x + x2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 4x + x2 = 2.125 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 2.125 + 4 Reorder the terms: 4 + 4x + x2 = 2.125 + 4 Combine like terms: 2.125 + 4 = 6.125 4 + 4x + x2 = 6.125 Factor a perfect square on the left side: (x + 2)(x + 2) = 6.125 Calculate the square root of the right side: 2.474873734 Break this problem into two subproblems by setting (x + 2) equal to 2.474873734 and -2.474873734.Subproblem 1
x + 2 = 2.474873734 Simplifying x + 2 = 2.474873734 Reorder the terms: 2 + x = 2.474873734 Solving 2 + x = 2.474873734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.474873734 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.474873734 + -2 x = 2.474873734 + -2 Combine like terms: 2.474873734 + -2 = 0.474873734 x = 0.474873734 Simplifying x = 0.474873734Subproblem 2
x + 2 = -2.474873734 Simplifying x + 2 = -2.474873734 Reorder the terms: 2 + x = -2.474873734 Solving 2 + x = -2.474873734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.474873734 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.474873734 + -2 x = -2.474873734 + -2 Combine like terms: -2.474873734 + -2 = -4.474873734 x = -4.474873734 Simplifying x = -4.474873734Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.474873734, -4.474873734}
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