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Simplifying (x2 + -130x + -8000) = 0 Reorder the terms: (-8000 + -130x + x2) = 0 Remove parenthesis around (-8000 + -130x + x2) -8000 + -130x + x2 = 0 Solving -8000 + -130x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8000' to each side of the equation. -8000 + -130x + 8000 + x2 = 0 + 8000 Reorder the terms: -8000 + 8000 + -130x + x2 = 0 + 8000 Combine like terms: -8000 + 8000 = 0 0 + -130x + x2 = 0 + 8000 -130x + x2 = 0 + 8000 Combine like terms: 0 + 8000 = 8000 -130x + x2 = 8000 The x term is -130x. Take half its coefficient (-65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. -130x + 4225 + x2 = 8000 + 4225 Reorder the terms: 4225 + -130x + x2 = 8000 + 4225 Combine like terms: 8000 + 4225 = 12225 4225 + -130x + x2 = 12225 Factor a perfect square on the left side: (x + -65)(x + -65) = 12225 Calculate the square root of the right side: 110.566721937 Break this problem into two subproblems by setting (x + -65) equal to 110.566721937 and -110.566721937.Subproblem 1
x + -65 = 110.566721937 Simplifying x + -65 = 110.566721937 Reorder the terms: -65 + x = 110.566721937 Solving -65 + x = 110.566721937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = 110.566721937 + 65 Combine like terms: -65 + 65 = 0 0 + x = 110.566721937 + 65 x = 110.566721937 + 65 Combine like terms: 110.566721937 + 65 = 175.566721937 x = 175.566721937 Simplifying x = 175.566721937Subproblem 2
x + -65 = -110.566721937 Simplifying x + -65 = -110.566721937 Reorder the terms: -65 + x = -110.566721937 Solving -65 + x = -110.566721937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = -110.566721937 + 65 Combine like terms: -65 + 65 = 0 0 + x = -110.566721937 + 65 x = -110.566721937 + 65 Combine like terms: -110.566721937 + 65 = -45.566721937 x = -45.566721937 Simplifying x = -45.566721937Solution
The solution to the problem is based on the solutions from the subproblems. x = {175.566721937, -45.566721937}
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