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Simplifying (x) = x2 + 5x + -250 x = x2 + 5x + -250 Reorder the terms: x = -250 + 5x + x2 Solving x = -250 + 5x + x2 Solving for variable 'x'. Reorder the terms: 250 + x + -5x + -1x2 = -250 + 5x + x2 + 250 + -5x + -1x2 Combine like terms: x + -5x = -4x 250 + -4x + -1x2 = -250 + 5x + x2 + 250 + -5x + -1x2 Reorder the terms: 250 + -4x + -1x2 = -250 + 250 + 5x + -5x + x2 + -1x2 Combine like terms: -250 + 250 = 0 250 + -4x + -1x2 = 0 + 5x + -5x + x2 + -1x2 250 + -4x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 250 + -4x + -1x2 = 0 + x2 + -1x2 250 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 250 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -250 + 4x + x2 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + 4x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 4x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 4x + x2 = 0 + 250 4x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 4x + x2 = 250 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 250 + 4 Reorder the terms: 4 + 4x + x2 = 250 + 4 Combine like terms: 250 + 4 = 254 4 + 4x + x2 = 254 Factor a perfect square on the left side: (x + 2)(x + 2) = 254 Calculate the square root of the right side: 15.937377451 Break this problem into two subproblems by setting (x + 2) equal to 15.937377451 and -15.937377451.Subproblem 1
x + 2 = 15.937377451 Simplifying x + 2 = 15.937377451 Reorder the terms: 2 + x = 15.937377451 Solving 2 + x = 15.937377451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 15.937377451 + -2 Combine like terms: 2 + -2 = 0 0 + x = 15.937377451 + -2 x = 15.937377451 + -2 Combine like terms: 15.937377451 + -2 = 13.937377451 x = 13.937377451 Simplifying x = 13.937377451Subproblem 2
x + 2 = -15.937377451 Simplifying x + 2 = -15.937377451 Reorder the terms: 2 + x = -15.937377451 Solving 2 + x = -15.937377451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -15.937377451 + -2 Combine like terms: 2 + -2 = 0 0 + x = -15.937377451 + -2 x = -15.937377451 + -2 Combine like terms: -15.937377451 + -2 = -17.937377451 x = -17.937377451 Simplifying x = -17.937377451Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.937377451, -17.937377451}
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