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Simplifying -0.004x2 + x + 2.5 = 0 Reorder the terms: 2.5 + x + -0.004x2 = 0 Solving 2.5 + x + -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'. -625 + -250x + x2 = 0 Move the constant term to the right: Add '625' to each side of the equation. -625 + -250x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + -250x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + -250x + x2 = 0 + 625 -250x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 -250x + x2 = 625 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -250x + 0.25 + x2 = 625 + 0.25 Reorder the terms: 0.25 + -250x + x2 = 625 + 0.25 Combine like terms: 625 + 0.25 = 625.25 0.25 + -250x + x2 = 625.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 625.25 Calculate the square root of the right side: 25.0049995 Break this problem into two subproblems by setting (x + 0.5) equal to 25.0049995 and -25.0049995.Subproblem 1
x + 0.5 = 25.0049995 Simplifying x + 0.5 = 25.0049995 Reorder the terms: 0.5 + x = 25.0049995 Solving 0.5 + x = 25.0049995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 25.0049995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 25.0049995 + -0.5 x = 25.0049995 + -0.5 Combine like terms: 25.0049995 + -0.5 = 24.5049995 x = 24.5049995 Simplifying x = 24.5049995Subproblem 2
x + 0.5 = -25.0049995 Simplifying x + 0.5 = -25.0049995 Reorder the terms: 0.5 + x = -25.0049995 Solving 0.5 + x = -25.0049995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -25.0049995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -25.0049995 + -0.5 x = -25.0049995 + -0.5 Combine like terms: -25.0049995 + -0.5 = -25.5049995 x = -25.5049995 Simplifying x = -25.5049995Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.5049995, -25.5049995}
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