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Simplifying 0.25x2 + -8x + -6000 = 0 Reorder the terms: -6000 + -8x + 0.25x2 = 0 Solving -6000 + -8x + 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'. -24000 + -32x + x2 = 0 Move the constant term to the right: Add '24000' to each side of the equation. -24000 + -32x + 24000 + x2 = 0 + 24000 Reorder the terms: -24000 + 24000 + -32x + x2 = 0 + 24000 Combine like terms: -24000 + 24000 = 0 0 + -32x + x2 = 0 + 24000 -32x + x2 = 0 + 24000 Combine like terms: 0 + 24000 = 24000 -32x + x2 = 24000 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = 24000 + 256 Reorder the terms: 256 + -32x + x2 = 24000 + 256 Combine like terms: 24000 + 256 = 24256 256 + -32x + x2 = 24256 Factor a perfect square on the left side: (x + -16)(x + -16) = 24256 Calculate the square root of the right side: 155.743378671 Break this problem into two subproblems by setting (x + -16) equal to 155.743378671 and -155.743378671.Subproblem 1
x + -16 = 155.743378671 Simplifying x + -16 = 155.743378671 Reorder the terms: -16 + x = 155.743378671 Solving -16 + x = 155.743378671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 155.743378671 + 16 Combine like terms: -16 + 16 = 0 0 + x = 155.743378671 + 16 x = 155.743378671 + 16 Combine like terms: 155.743378671 + 16 = 171.743378671 x = 171.743378671 Simplifying x = 171.743378671Subproblem 2
x + -16 = -155.743378671 Simplifying x + -16 = -155.743378671 Reorder the terms: -16 + x = -155.743378671 Solving -16 + x = -155.743378671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -155.743378671 + 16 Combine like terms: -16 + 16 = 0 0 + x = -155.743378671 + 16 x = -155.743378671 + 16 Combine like terms: -155.743378671 + 16 = -139.743378671 x = -139.743378671 Simplifying x = -139.743378671Solution
The solution to the problem is based on the solutions from the subproblems. x = {171.743378671, -139.743378671}
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