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Simplifying 0.8x2 + -24x + 250x = 25 Reorder the terms: -24x + 250x + 0.8x2 = 25 Combine like terms: -24x + 250x = 226x 226x + 0.8x2 = 25 Solving 226x + 0.8x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 226x + 0.8x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 226x + 0.8x2 = 0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -31.25 + 282.5x + x2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + 282.5x + 31.25 + x2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + 282.5x + x2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + 282.5x + x2 = 0 + 31.25 282.5x + x2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 282.5x + x2 = 31.25 The x term is 282.5x. Take half its coefficient (141.25). Square it (19951.5625) and add it to both sides. Add '19951.5625' to each side of the equation. 282.5x + 19951.5625 + x2 = 31.25 + 19951.5625 Reorder the terms: 19951.5625 + 282.5x + x2 = 31.25 + 19951.5625 Combine like terms: 31.25 + 19951.5625 = 19982.8125 19951.5625 + 282.5x + x2 = 19982.8125 Factor a perfect square on the left side: (x + 141.25)(x + 141.25) = 19982.8125 Calculate the square root of the right side: 141.360576187 Break this problem into two subproblems by setting (x + 141.25) equal to 141.360576187 and -141.360576187.Subproblem 1
x + 141.25 = 141.360576187 Simplifying x + 141.25 = 141.360576187 Reorder the terms: 141.25 + x = 141.360576187 Solving 141.25 + x = 141.360576187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-141.25' to each side of the equation. 141.25 + -141.25 + x = 141.360576187 + -141.25 Combine like terms: 141.25 + -141.25 = 0.00 0.00 + x = 141.360576187 + -141.25 x = 141.360576187 + -141.25 Combine like terms: 141.360576187 + -141.25 = 0.110576187 x = 0.110576187 Simplifying x = 0.110576187Subproblem 2
x + 141.25 = -141.360576187 Simplifying x + 141.25 = -141.360576187 Reorder the terms: 141.25 + x = -141.360576187 Solving 141.25 + x = -141.360576187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-141.25' to each side of the equation. 141.25 + -141.25 + x = -141.360576187 + -141.25 Combine like terms: 141.25 + -141.25 = 0.00 0.00 + x = -141.360576187 + -141.25 x = -141.360576187 + -141.25 Combine like terms: -141.360576187 + -141.25 = -282.610576187 x = -282.610576187 Simplifying x = -282.610576187Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.110576187, -282.610576187}
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