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Simplifying 0.25x2 + 4x + -8 = 0 Reorder the terms: -8 + 4x + 0.25x2 = 0 Solving -8 + 4x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -32 + 16x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 16x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 16x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 16x + x2 = 0 + 32 16x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 16x + x2 = 32 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 32 + 64 Reorder the terms: 64 + 16x + x2 = 32 + 64 Combine like terms: 32 + 64 = 96 64 + 16x + x2 = 96 Factor a perfect square on the left side: (x + 8)(x + 8) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 8) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 8 = 9.797958971 Simplifying x + 8 = 9.797958971 Reorder the terms: 8 + x = 9.797958971 Solving 8 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 9.797958971 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.797958971 + -8 x = 9.797958971 + -8 Combine like terms: 9.797958971 + -8 = 1.797958971 x = 1.797958971 Simplifying x = 1.797958971Subproblem 2
x + 8 = -9.797958971 Simplifying x + 8 = -9.797958971 Reorder the terms: 8 + x = -9.797958971 Solving 8 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -9.797958971 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.797958971 + -8 x = -9.797958971 + -8 Combine like terms: -9.797958971 + -8 = -17.797958971 x = -17.797958971 Simplifying x = -17.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.797958971, -17.797958971}
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