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Simplifying x(0.25x + -1) + -8 = 0 Reorder the terms: x(-1 + 0.25x) + -8 = 0 (-1 * x + 0.25x * x) + -8 = 0 (-1x + 0.25x2) + -8 = 0 Reorder the terms: -8 + -1x + 0.25x2 = 0 Solving -8 + -1x + 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 + -4x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -4x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -4x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -4x + x2 = 0 + 32 -4x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -4x + x2 = 32 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 = 32 + 4 Reorder the terms: 4 + -4x + x2 = 32 + 4 Combine like terms: 32 + 4 = 36 4 + -4x + x2 = 36 Factor a perfect square on the left side: (x + -2)(x + -2) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + -2) equal to 6 and -6.Subproblem 1
x + -2 = 6 Simplifying x + -2 = 6 Reorder the terms: -2 + x = 6 Solving -2 + x = 6 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 = 6 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6 + 2 x = 6 + 2 Combine like terms: 6 + 2 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -2 = -6 Simplifying x + -2 = -6 Reorder the terms: -2 + x = -6 Solving -2 + x = -6 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 = -6 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6 + 2 x = -6 + 2 Combine like terms: -6 + 2 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -4}
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