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Simplifying x + 250 = (2x)(2x) Reorder the terms: 250 + x = (2x)(2x) Remove parenthesis around (2x) 250 + x = 2x(2x) Remove parenthesis around (2x) 250 + x = 2x * 2x Reorder the terms for easier multiplication: 250 + x = 2 * 2x * x Multiply 2 * 2 250 + x = 4x * x Multiply x * x 250 + x = 4x2 Solving 250 + x = 4x2 Solving for variable 'x'. Combine like terms: 4x2 + -4x2 = 0 250 + x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -62.5 + -0.25x + x2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + -0.25x + 62.5 + x2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + -0.25x + x2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + -0.25x + x2 = 0 + 62.5 -0.25x + x2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 -0.25x + x2 = 62.5 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. -0.25x + 0.25 + x2 = 62.5 + 0.25 Reorder the terms: 0.25 + -0.25x + x2 = 62.5 + 0.25 Combine like terms: 62.5 + 0.25 = 62.75 0.25 + -0.25x + x2 = 62.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 62.75 Calculate the square root of the right side: 7.921489759 Break this problem into two subproblems by setting (x + 0.5) equal to 7.921489759 and -7.921489759.Subproblem 1
x + 0.5 = 7.921489759 Simplifying x + 0.5 = 7.921489759 Reorder the terms: 0.5 + x = 7.921489759 Solving 0.5 + x = 7.921489759 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 = 7.921489759 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.921489759 + -0.5 x = 7.921489759 + -0.5 Combine like terms: 7.921489759 + -0.5 = 7.421489759 x = 7.421489759 Simplifying x = 7.421489759Subproblem 2
x + 0.5 = -7.921489759 Simplifying x + 0.5 = -7.921489759 Reorder the terms: 0.5 + x = -7.921489759 Solving 0.5 + x = -7.921489759 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 = -7.921489759 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.921489759 + -0.5 x = -7.921489759 + -0.5 Combine like terms: -7.921489759 + -0.5 = -8.421489759 x = -8.421489759 Simplifying x = -8.421489759Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.421489759, -8.421489759}
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