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Simplifying 8x2 + 7x + -25 = 0 Reorder the terms: -25 + 7x + 8x2 = 0 Solving -25 + 7x + 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'. -3.125 + 0.875x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 0.875x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 0.875x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 0.875x + x2 = 0 + 3.125 0.875x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 0.875x + x2 = 3.125 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = 3.125 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = 3.125 + 0.19140625 Combine like terms: 3.125 + 0.19140625 = 3.31640625 0.19140625 + 0.875x + x2 = 3.31640625 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 3.31640625 Calculate the square root of the right side: 1.821100286 Break this problem into two subproblems by setting (x + 0.4375) equal to 1.821100286 and -1.821100286.Subproblem 1
x + 0.4375 = 1.821100286 Simplifying x + 0.4375 = 1.821100286 Reorder the terms: 0.4375 + x = 1.821100286 Solving 0.4375 + x = 1.821100286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 1.821100286 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 1.821100286 + -0.4375 x = 1.821100286 + -0.4375 Combine like terms: 1.821100286 + -0.4375 = 1.383600286 x = 1.383600286 Simplifying x = 1.383600286Subproblem 2
x + 0.4375 = -1.821100286 Simplifying x + 0.4375 = -1.821100286 Reorder the terms: 0.4375 + x = -1.821100286 Solving 0.4375 + x = -1.821100286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -1.821100286 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -1.821100286 + -0.4375 x = -1.821100286 + -0.4375 Combine like terms: -1.821100286 + -0.4375 = -2.258600286 x = -2.258600286 Simplifying x = -2.258600286Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.383600286, -2.258600286}
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