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Simplifying x2 + 30x + -500 = 0 Reorder the terms: -500 + 30x + x2 = 0 Solving -500 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + 30x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 30x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 30x + x2 = 0 + 500 30x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 30x + x2 = 500 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 500 + 225 Reorder the terms: 225 + 30x + x2 = 500 + 225 Combine like terms: 500 + 225 = 725 225 + 30x + x2 = 725 Factor a perfect square on the left side: (x + 15)(x + 15) = 725 Calculate the square root of the right side: 26.925824036 Break this problem into two subproblems by setting (x + 15) equal to 26.925824036 and -26.925824036.Subproblem 1
x + 15 = 26.925824036 Simplifying x + 15 = 26.925824036 Reorder the terms: 15 + x = 26.925824036 Solving 15 + x = 26.925824036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 26.925824036 + -15 Combine like terms: 15 + -15 = 0 0 + x = 26.925824036 + -15 x = 26.925824036 + -15 Combine like terms: 26.925824036 + -15 = 11.925824036 x = 11.925824036 Simplifying x = 11.925824036Subproblem 2
x + 15 = -26.925824036 Simplifying x + 15 = -26.925824036 Reorder the terms: 15 + x = -26.925824036 Solving 15 + x = -26.925824036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -26.925824036 + -15 Combine like terms: 15 + -15 = 0 0 + x = -26.925824036 + -15 x = -26.925824036 + -15 Combine like terms: -26.925824036 + -15 = -41.925824036 x = -41.925824036 Simplifying x = -41.925824036Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.925824036, -41.925824036}
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