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Simplifying 39.25 = x2 + x Reorder the terms: 39.25 = x + x2 Solving 39.25 = x + x2 Solving for variable 'x'. Reorder the terms: 39.25 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 39.25 + -1x + -1x2 = 0 + x2 + -1x2 39.25 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 39.25 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -39.25 + x + x2 = 0 Move the constant term to the right: Add '39.25' to each side of the equation. -39.25 + x + 39.25 + x2 = 0 + 39.25 Reorder the terms: -39.25 + 39.25 + x + x2 = 0 + 39.25 Combine like terms: -39.25 + 39.25 = 0.00 0.00 + x + x2 = 0 + 39.25 x + x2 = 0 + 39.25 Combine like terms: 0 + 39.25 = 39.25 x + x2 = 39.25 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. + 0.25 + x2 = 39.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 39.25 + 0.25 Combine like terms: 39.25 + 0.25 = 39.5 1.25 + x2 = 39.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 39.5 Calculate the square root of the right side: 6.284902545 Break this problem into two subproblems by setting (x + 0.5) equal to 6.284902545 and -6.284902545.Subproblem 1
x + 0.5 = 6.284902545 Simplifying x + 0.5 = 6.284902545 Reorder the terms: 0.5 + x = 6.284902545 Solving 0.5 + x = 6.284902545 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 = 6.284902545 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.284902545 + -0.5 x = 6.284902545 + -0.5 Combine like terms: 6.284902545 + -0.5 = 5.784902545 x = 5.784902545 Simplifying x = 5.784902545Subproblem 2
x + 0.5 = -6.284902545 Simplifying x + 0.5 = -6.284902545 Reorder the terms: 0.5 + x = -6.284902545 Solving 0.5 + x = -6.284902545 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 = -6.284902545 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.284902545 + -0.5 x = -6.284902545 + -0.5 Combine like terms: -6.284902545 + -0.5 = -6.784902545 x = -6.784902545 Simplifying x = -6.784902545Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.784902545, -6.784902545}
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