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Simplifying x2 + 44x + -315 = 0 Reorder the terms: -315 + 44x + x2 = 0 Solving -315 + 44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '315' to each side of the equation. -315 + 44x + 315 + x2 = 0 + 315 Reorder the terms: -315 + 315 + 44x + x2 = 0 + 315 Combine like terms: -315 + 315 = 0 0 + 44x + x2 = 0 + 315 44x + x2 = 0 + 315 Combine like terms: 0 + 315 = 315 44x + x2 = 315 The x term is 44x. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x + 484 + x2 = 315 + 484 Reorder the terms: 484 + 44x + x2 = 315 + 484 Combine like terms: 315 + 484 = 799 484 + 44x + x2 = 799 Factor a perfect square on the left side: (x + 22)(x + 22) = 799 Calculate the square root of the right side: 28.26658805 Break this problem into two subproblems by setting (x + 22) equal to 28.26658805 and -28.26658805.Subproblem 1
x + 22 = 28.26658805 Simplifying x + 22 = 28.26658805 Reorder the terms: 22 + x = 28.26658805 Solving 22 + x = 28.26658805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 28.26658805 + -22 Combine like terms: 22 + -22 = 0 0 + x = 28.26658805 + -22 x = 28.26658805 + -22 Combine like terms: 28.26658805 + -22 = 6.26658805 x = 6.26658805 Simplifying x = 6.26658805Subproblem 2
x + 22 = -28.26658805 Simplifying x + 22 = -28.26658805 Reorder the terms: 22 + x = -28.26658805 Solving 22 + x = -28.26658805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = -28.26658805 + -22 Combine like terms: 22 + -22 = 0 0 + x = -28.26658805 + -22 x = -28.26658805 + -22 Combine like terms: -28.26658805 + -22 = -50.26658805 x = -50.26658805 Simplifying x = -50.26658805Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.26658805, -50.26658805}
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