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Simplifying 0 = x2 + -10x + -13270 Reorder the terms: 0 = -13270 + -10x + x2 Solving 0 = -13270 + -10x + x2 Solving for variable 'x'. Combine like terms: 0 + 13270 = 13270 13270 + 10x + -1x2 = -13270 + -10x + x2 + 13270 + 10x + -1x2 Reorder the terms: 13270 + 10x + -1x2 = -13270 + 13270 + -10x + 10x + x2 + -1x2 Combine like terms: -13270 + 13270 = 0 13270 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2 13270 + 10x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 13270 + 10x + -1x2 = 0 + x2 + -1x2 13270 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 13270 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13270 + -10x + x2 = 0 Move the constant term to the right: Add '13270' to each side of the equation. -13270 + -10x + 13270 + x2 = 0 + 13270 Reorder the terms: -13270 + 13270 + -10x + x2 = 0 + 13270 Combine like terms: -13270 + 13270 = 0 0 + -10x + x2 = 0 + 13270 -10x + x2 = 0 + 13270 Combine like terms: 0 + 13270 = 13270 -10x + x2 = 13270 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 13270 + 25 Reorder the terms: 25 + -10x + x2 = 13270 + 25 Combine like terms: 13270 + 25 = 13295 25 + -10x + x2 = 13295 Factor a perfect square on the left side: (x + -5)(x + -5) = 13295 Calculate the square root of the right side: 115.30394616 Break this problem into two subproblems by setting (x + -5) equal to 115.30394616 and -115.30394616.Subproblem 1
x + -5 = 115.30394616 Simplifying x + -5 = 115.30394616 Reorder the terms: -5 + x = 115.30394616 Solving -5 + x = 115.30394616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 115.30394616 + 5 Combine like terms: -5 + 5 = 0 0 + x = 115.30394616 + 5 x = 115.30394616 + 5 Combine like terms: 115.30394616 + 5 = 120.30394616 x = 120.30394616 Simplifying x = 120.30394616Subproblem 2
x + -5 = -115.30394616 Simplifying x + -5 = -115.30394616 Reorder the terms: -5 + x = -115.30394616 Solving -5 + x = -115.30394616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -115.30394616 + 5 Combine like terms: -5 + 5 = 0 0 + x = -115.30394616 + 5 x = -115.30394616 + 5 Combine like terms: -115.30394616 + 5 = -110.30394616 x = -110.30394616 Simplifying x = -110.30394616Solution
The solution to the problem is based on the solutions from the subproblems. x = {120.30394616, -110.30394616}
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