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Simplifying 0 = x2 + 26x + -600 Reorder the terms: 0 = -600 + 26x + x2 Solving 0 = -600 + 26x + x2 Solving for variable 'x'. Combine like terms: 0 + 600 = 600 600 + -26x + -1x2 = -600 + 26x + x2 + 600 + -26x + -1x2 Reorder the terms: 600 + -26x + -1x2 = -600 + 600 + 26x + -26x + x2 + -1x2 Combine like terms: -600 + 600 = 0 600 + -26x + -1x2 = 0 + 26x + -26x + x2 + -1x2 600 + -26x + -1x2 = 26x + -26x + x2 + -1x2 Combine like terms: 26x + -26x = 0 600 + -26x + -1x2 = 0 + x2 + -1x2 600 + -26x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 600 + -26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -600 + 26x + x2 = 0 Move the constant term to the right: Add '600' to each side of the equation. -600 + 26x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + 26x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + 26x + x2 = 0 + 600 26x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 26x + x2 = 600 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = 600 + 169 Reorder the terms: 169 + 26x + x2 = 600 + 169 Combine like terms: 600 + 169 = 769 169 + 26x + x2 = 769 Factor a perfect square on the left side: (x + 13)(x + 13) = 769 Calculate the square root of the right side: 27.730849248 Break this problem into two subproblems by setting (x + 13) equal to 27.730849248 and -27.730849248.Subproblem 1
x + 13 = 27.730849248 Simplifying x + 13 = 27.730849248 Reorder the terms: 13 + x = 27.730849248 Solving 13 + x = 27.730849248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 27.730849248 + -13 Combine like terms: 13 + -13 = 0 0 + x = 27.730849248 + -13 x = 27.730849248 + -13 Combine like terms: 27.730849248 + -13 = 14.730849248 x = 14.730849248 Simplifying x = 14.730849248Subproblem 2
x + 13 = -27.730849248 Simplifying x + 13 = -27.730849248 Reorder the terms: 13 + x = -27.730849248 Solving 13 + x = -27.730849248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -27.730849248 + -13 Combine like terms: 13 + -13 = 0 0 + x = -27.730849248 + -13 x = -27.730849248 + -13 Combine like terms: -27.730849248 + -13 = -40.730849248 x = -40.730849248 Simplifying x = -40.730849248Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.730849248, -40.730849248}
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