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Simplifying 60.07 = x + x2 Solving 60.07 = x + x2 Solving for variable 'x'. Reorder the terms: 60.07 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 60.07 + -1x + -1x2 = 0 + x2 + -1x2 60.07 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 60.07 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60.07 + x + x2 = 0 Move the constant term to the right: Add '60.07' to each side of the equation. -60.07 + x + 60.07 + x2 = 0 + 60.07 Reorder the terms: -60.07 + 60.07 + x + x2 = 0 + 60.07 Combine like terms: -60.07 + 60.07 = 0.00 0.00 + x + x2 = 0 + 60.07 x + x2 = 0 + 60.07 Combine like terms: 0 + 60.07 = 60.07 x + x2 = 60.07 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 = 60.07 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 60.07 + 0.25 Combine like terms: 60.07 + 0.25 = 60.32 1.25 + x2 = 60.32 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 60.32 Calculate the square root of the right side: 7.766595136 Break this problem into two subproblems by setting (x + 0.5) equal to 7.766595136 and -7.766595136.Subproblem 1
x + 0.5 = 7.766595136 Simplifying x + 0.5 = 7.766595136 Reorder the terms: 0.5 + x = 7.766595136 Solving 0.5 + x = 7.766595136 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 = 7.766595136 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.766595136 + -0.5 x = 7.766595136 + -0.5 Combine like terms: 7.766595136 + -0.5 = 7.266595136 x = 7.266595136 Simplifying x = 7.266595136Subproblem 2
x + 0.5 = -7.766595136 Simplifying x + 0.5 = -7.766595136 Reorder the terms: 0.5 + x = -7.766595136 Solving 0.5 + x = -7.766595136 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 = -7.766595136 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.766595136 + -0.5 x = -7.766595136 + -0.5 Combine like terms: -7.766595136 + -0.5 = -8.266595136 x = -8.266595136 Simplifying x = -8.266595136Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.266595136, -8.266595136}
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