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Simplifying -0.25x2 + 4x = -2 Reorder the terms: 4x + -0.25x2 = -2 Solving 4x + -0.25x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 4x + -0.25x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 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'. -8 + -16x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -16x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -16x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -16x + x2 = 0 + 8 -16x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -16x + x2 = 8 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 = 8 + 64 Reorder the terms: 64 + -16x + x2 = 8 + 64 Combine like terms: 8 + 64 = 72 64 + -16x + x2 = 72 Factor a perfect square on the left side: (x + -8)(x + -8) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + -8) equal to 8.485281374 and -8.485281374.Subproblem 1
x + -8 = 8.485281374 Simplifying x + -8 = 8.485281374 Reorder the terms: -8 + x = 8.485281374 Solving -8 + x = 8.485281374 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 = 8.485281374 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.485281374 + 8 x = 8.485281374 + 8 Combine like terms: 8.485281374 + 8 = 16.485281374 x = 16.485281374 Simplifying x = 16.485281374Subproblem 2
x + -8 = -8.485281374 Simplifying x + -8 = -8.485281374 Reorder the terms: -8 + x = -8.485281374 Solving -8 + x = -8.485281374 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 = -8.485281374 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.485281374 + 8 x = -8.485281374 + 8 Combine like terms: -8.485281374 + 8 = -0.485281374 x = -0.485281374 Simplifying x = -0.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.485281374, -0.485281374}
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