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Simplifying 60 + 5x = x2 + -14 Reorder the terms: 60 + 5x = -14 + x2 Solving 60 + 5x = -14 + x2 Solving for variable 'x'. Reorder the terms: 60 + 14 + 5x + -1x2 = -14 + x2 + 14 + -1x2 Combine like terms: 60 + 14 = 74 74 + 5x + -1x2 = -14 + x2 + 14 + -1x2 Reorder the terms: 74 + 5x + -1x2 = -14 + 14 + x2 + -1x2 Combine like terms: -14 + 14 = 0 74 + 5x + -1x2 = 0 + x2 + -1x2 74 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 74 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -74 + -5x + x2 = 0 Move the constant term to the right: Add '74' to each side of the equation. -74 + -5x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + -5x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -5x + x2 = 0 + 74 -5x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 -5x + x2 = 74 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 74 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 74 + 6.25 Combine like terms: 74 + 6.25 = 80.25 6.25 + -5x + x2 = 80.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + -2.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + -2.5 = 8.958236434 Simplifying x + -2.5 = 8.958236434 Reorder the terms: -2.5 + x = 8.958236434 Solving -2.5 + x = 8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 8.958236434 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 8.958236434 + 2.5 x = 8.958236434 + 2.5 Combine like terms: 8.958236434 + 2.5 = 11.458236434 x = 11.458236434 Simplifying x = 11.458236434Subproblem 2
x + -2.5 = -8.958236434 Simplifying x + -2.5 = -8.958236434 Reorder the terms: -2.5 + x = -8.958236434 Solving -2.5 + x = -8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -8.958236434 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -8.958236434 + 2.5 x = -8.958236434 + 2.5 Combine like terms: -8.958236434 + 2.5 = -6.458236434 x = -6.458236434 Simplifying x = -6.458236434Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.458236434, -6.458236434}
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