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Simplifying 2x2 + 70x = 1600 Reorder the terms: 70x + 2x2 = 1600 Solving 70x + 2x2 = 1600 Solving for variable 'x'. Reorder the terms: -1600 + 70x + 2x2 = 1600 + -1600 Combine like terms: 1600 + -1600 = 0 -1600 + 70x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-800 + 35x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-800 + 35x + x2)' equal to zero and attempt to solve: Simplifying -800 + 35x + x2 = 0 Solving -800 + 35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '800' to each side of the equation. -800 + 35x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + 35x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 35x + x2 = 0 + 800 35x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 35x + x2 = 800 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 800 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 800 + 306.25 Combine like terms: 800 + 306.25 = 1106.25 306.25 + 35x + x2 = 1106.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 1106.25 Calculate the square root of the right side: 33.260336739 Break this problem into two subproblems by setting (x + 17.5) equal to 33.260336739 and -33.260336739.Subproblem 1
x + 17.5 = 33.260336739 Simplifying x + 17.5 = 33.260336739 Reorder the terms: 17.5 + x = 33.260336739 Solving 17.5 + x = 33.260336739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 33.260336739 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 33.260336739 + -17.5 x = 33.260336739 + -17.5 Combine like terms: 33.260336739 + -17.5 = 15.760336739 x = 15.760336739 Simplifying x = 15.760336739Subproblem 2
x + 17.5 = -33.260336739 Simplifying x + 17.5 = -33.260336739 Reorder the terms: 17.5 + x = -33.260336739 Solving 17.5 + x = -33.260336739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -33.260336739 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -33.260336739 + -17.5 x = -33.260336739 + -17.5 Combine like terms: -33.260336739 + -17.5 = -50.760336739 x = -50.760336739 Simplifying x = -50.760336739Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.760336739, -50.760336739}Solution
x = {15.760336739, -50.760336739}
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