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Simplifying x2 + -140x + -1200 = 0 Reorder the terms: -1200 + -140x + x2 = 0 Solving -1200 + -140x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + -140x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + -140x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + -140x + x2 = 0 + 1200 -140x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 -140x + x2 = 1200 The x term is -140x. Take half its coefficient (-70). Square it (4900) and add it to both sides. Add '4900' to each side of the equation. -140x + 4900 + x2 = 1200 + 4900 Reorder the terms: 4900 + -140x + x2 = 1200 + 4900 Combine like terms: 1200 + 4900 = 6100 4900 + -140x + x2 = 6100 Factor a perfect square on the left side: (x + -70)(x + -70) = 6100 Calculate the square root of the right side: 78.102496759 Break this problem into two subproblems by setting (x + -70) equal to 78.102496759 and -78.102496759.Subproblem 1
x + -70 = 78.102496759 Simplifying x + -70 = 78.102496759 Reorder the terms: -70 + x = 78.102496759 Solving -70 + x = 78.102496759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = 78.102496759 + 70 Combine like terms: -70 + 70 = 0 0 + x = 78.102496759 + 70 x = 78.102496759 + 70 Combine like terms: 78.102496759 + 70 = 148.102496759 x = 148.102496759 Simplifying x = 148.102496759Subproblem 2
x + -70 = -78.102496759 Simplifying x + -70 = -78.102496759 Reorder the terms: -70 + x = -78.102496759 Solving -70 + x = -78.102496759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = -78.102496759 + 70 Combine like terms: -70 + 70 = 0 0 + x = -78.102496759 + 70 x = -78.102496759 + 70 Combine like terms: -78.102496759 + 70 = -8.102496759 x = -8.102496759 Simplifying x = -8.102496759Solution
The solution to the problem is based on the solutions from the subproblems. x = {148.102496759, -8.102496759}
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