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Simplifying x(0.25x + -2) = 252 Reorder the terms: x(-2 + 0.25x) = 252 (-2 * x + 0.25x * x) = 252 (-2x + 0.25x2) = 252 Solving -2x + 0.25x2 = 252 Solving for variable 'x'. Reorder the terms: -252 + -2x + 0.25x2 = 252 + -252 Combine like terms: 252 + -252 = 0 -252 + -2x + 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'. -1008 + -8x + x2 = 0 Move the constant term to the right: Add '1008' to each side of the equation. -1008 + -8x + 1008 + x2 = 0 + 1008 Reorder the terms: -1008 + 1008 + -8x + x2 = 0 + 1008 Combine like terms: -1008 + 1008 = 0 0 + -8x + x2 = 0 + 1008 -8x + x2 = 0 + 1008 Combine like terms: 0 + 1008 = 1008 -8x + x2 = 1008 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 1008 + 16 Reorder the terms: 16 + -8x + x2 = 1008 + 16 Combine like terms: 1008 + 16 = 1024 16 + -8x + x2 = 1024 Factor a perfect square on the left side: (x + -4)(x + -4) = 1024 Calculate the square root of the right side: 32 Break this problem into two subproblems by setting (x + -4) equal to 32 and -32.Subproblem 1
x + -4 = 32 Simplifying x + -4 = 32 Reorder the terms: -4 + x = 32 Solving -4 + x = 32 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 32 + 4 Combine like terms: -4 + 4 = 0 0 + x = 32 + 4 x = 32 + 4 Combine like terms: 32 + 4 = 36 x = 36 Simplifying x = 36Subproblem 2
x + -4 = -32 Simplifying x + -4 = -32 Reorder the terms: -4 + x = -32 Solving -4 + x = -32 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -32 + 4 Combine like terms: -4 + 4 = 0 0 + x = -32 + 4 x = -32 + 4 Combine like terms: -32 + 4 = -28 x = -28 Simplifying x = -28Solution
The solution to the problem is based on the solutions from the subproblems. x = {36, -28}
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