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Simplifying 2x2 + 140x + -11000 = 0 Reorder the terms: -11000 + 140x + 2x2 = 0 Solving -11000 + 140x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5500 + 70x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5500 + 70x + x2)' equal to zero and attempt to solve: Simplifying -5500 + 70x + x2 = 0 Solving -5500 + 70x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5500' to each side of the equation. -5500 + 70x + 5500 + x2 = 0 + 5500 Reorder the terms: -5500 + 5500 + 70x + x2 = 0 + 5500 Combine like terms: -5500 + 5500 = 0 0 + 70x + x2 = 0 + 5500 70x + x2 = 0 + 5500 Combine like terms: 0 + 5500 = 5500 70x + x2 = 5500 The x term is 70x. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70x + 1225 + x2 = 5500 + 1225 Reorder the terms: 1225 + 70x + x2 = 5500 + 1225 Combine like terms: 5500 + 1225 = 6725 1225 + 70x + x2 = 6725 Factor a perfect square on the left side: (x + 35)(x + 35) = 6725 Calculate the square root of the right side: 82.006097334 Break this problem into two subproblems by setting (x + 35) equal to 82.006097334 and -82.006097334.Subproblem 1
x + 35 = 82.006097334 Simplifying x + 35 = 82.006097334 Reorder the terms: 35 + x = 82.006097334 Solving 35 + x = 82.006097334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 82.006097334 + -35 Combine like terms: 35 + -35 = 0 0 + x = 82.006097334 + -35 x = 82.006097334 + -35 Combine like terms: 82.006097334 + -35 = 47.006097334 x = 47.006097334 Simplifying x = 47.006097334Subproblem 2
x + 35 = -82.006097334 Simplifying x + 35 = -82.006097334 Reorder the terms: 35 + x = -82.006097334 Solving 35 + x = -82.006097334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = -82.006097334 + -35 Combine like terms: 35 + -35 = 0 0 + x = -82.006097334 + -35 x = -82.006097334 + -35 Combine like terms: -82.006097334 + -35 = -117.006097334 x = -117.006097334 Simplifying x = -117.006097334Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.006097334, -117.006097334}Solution
x = {47.006097334, -117.006097334}
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