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Simplifying -0.25x2 + -5x + 10 = -1x + 5 Reorder the terms: 10 + -5x + -0.25x2 = -1x + 5 Reorder the terms: 10 + -5x + -0.25x2 = 5 + -1x Solving 10 + -5x + -0.25x2 = 5 + -1x Solving for variable 'x'. Reorder the terms: 10 + -5 + -5x + x + -0.25x2 = 5 + -1x + -5 + x Combine like terms: 10 + -5 = 5 5 + -5x + x + -0.25x2 = 5 + -1x + -5 + x Combine like terms: -5x + x = -4x 5 + -4x + -0.25x2 = 5 + -1x + -5 + x Reorder the terms: 5 + -4x + -0.25x2 = 5 + -5 + -1x + x Combine like terms: 5 + -5 = 0 5 + -4x + -0.25x2 = 0 + -1x + x 5 + -4x + -0.25x2 = -1x + x Combine like terms: -1x + x = 0 5 + -4x + -0.25x2 = 0 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -20 + 16x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 16x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 16x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 16x + x2 = 0 + 20 16x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 16x + x2 = 20 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 = 20 + 64 Reorder the terms: 64 + 16x + x2 = 20 + 64 Combine like terms: 20 + 64 = 84 64 + 16x + x2 = 84 Factor a perfect square on the left side: (x + 8)(x + 8) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + 8) equal to 9.16515139 and -9.16515139.Subproblem 1
x + 8 = 9.16515139 Simplifying x + 8 = 9.16515139 Reorder the terms: 8 + x = 9.16515139 Solving 8 + x = 9.16515139 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 = 9.16515139 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.16515139 + -8 x = 9.16515139 + -8 Combine like terms: 9.16515139 + -8 = 1.16515139 x = 1.16515139 Simplifying x = 1.16515139Subproblem 2
x + 8 = -9.16515139 Simplifying x + 8 = -9.16515139 Reorder the terms: 8 + x = -9.16515139 Solving 8 + x = -9.16515139 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 = -9.16515139 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.16515139 + -8 x = -9.16515139 + -8 Combine like terms: -9.16515139 + -8 = -17.16515139 x = -17.16515139 Simplifying x = -17.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.16515139, -17.16515139}
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