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Simplifying 0.004x2 + -250x + 2500 = 0 Reorder the terms: 2500 + -250x + 0.004x2 = 0 Solving 2500 + -250x + 0.004x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.004 the coefficient of the squared term: Divide each side by '0.004'. 625000 + -62500x + x2 = 0 Move the constant term to the right: Add '-625000' to each side of the equation. 625000 + -62500x + -625000 + x2 = 0 + -625000 Reorder the terms: 625000 + -625000 + -62500x + x2 = 0 + -625000 Combine like terms: 625000 + -625000 = 0 0 + -62500x + x2 = 0 + -625000 -62500x + x2 = 0 + -625000 Combine like terms: 0 + -625000 = -625000 -62500x + x2 = -625000 The x term is -62500x. Take half its coefficient (-31250). Square it (976562500) and add it to both sides. Add '976562500' to each side of the equation. -62500x + 976562500 + x2 = -625000 + 976562500 Reorder the terms: 976562500 + -62500x + x2 = -625000 + 976562500 Combine like terms: -625000 + 976562500 = 975937500 976562500 + -62500x + x2 = 975937500 Factor a perfect square on the left side: (x + -31250)(x + -31250) = 975937500 Calculate the square root of the right side: 31239.998399488 Break this problem into two subproblems by setting (x + -31250) equal to 31239.998399488 and -31239.998399488.Subproblem 1
x + -31250 = 31239.998399488 Simplifying x + -31250 = 31239.998399488 Reorder the terms: -31250 + x = 31239.998399488 Solving -31250 + x = 31239.998399488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31250' to each side of the equation. -31250 + 31250 + x = 31239.998399488 + 31250 Combine like terms: -31250 + 31250 = 0 0 + x = 31239.998399488 + 31250 x = 31239.998399488 + 31250 Combine like terms: 31239.998399488 + 31250 = 62489.998399488 x = 62489.998399488 Simplifying x = 62489.998399488Subproblem 2
x + -31250 = -31239.998399488 Simplifying x + -31250 = -31239.998399488 Reorder the terms: -31250 + x = -31239.998399488 Solving -31250 + x = -31239.998399488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31250' to each side of the equation. -31250 + 31250 + x = -31239.998399488 + 31250 Combine like terms: -31250 + 31250 = 0 0 + x = -31239.998399488 + 31250 x = -31239.998399488 + 31250 Combine like terms: -31239.998399488 + 31250 = 10.001600512 x = 10.001600512 Simplifying x = 10.001600512Solution
The solution to the problem is based on the solutions from the subproblems. x = {62489.998399488, 10.001600512}
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