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Simplifying 4x2 + -370x + 1800 = 0 Reorder the terms: 1800 + -370x + 4x2 = 0 Solving 1800 + -370x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(900 + -185x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(900 + -185x + 2x2)' equal to zero and attempt to solve: Simplifying 900 + -185x + 2x2 = 0 Solving 900 + -185x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 450 + -92.5x + x2 = 0 Move the constant term to the right: Add '-450' to each side of the equation. 450 + -92.5x + -450 + x2 = 0 + -450 Reorder the terms: 450 + -450 + -92.5x + x2 = 0 + -450 Combine like terms: 450 + -450 = 0 0 + -92.5x + x2 = 0 + -450 -92.5x + x2 = 0 + -450 Combine like terms: 0 + -450 = -450 -92.5x + x2 = -450 The x term is -92.5x. Take half its coefficient (-46.25). Square it (2139.0625) and add it to both sides. Add '2139.0625' to each side of the equation. -92.5x + 2139.0625 + x2 = -450 + 2139.0625 Reorder the terms: 2139.0625 + -92.5x + x2 = -450 + 2139.0625 Combine like terms: -450 + 2139.0625 = 1689.0625 2139.0625 + -92.5x + x2 = 1689.0625 Factor a perfect square on the left side: (x + -46.25)(x + -46.25) = 1689.0625 Calculate the square root of the right side: 41.098205557 Break this problem into two subproblems by setting (x + -46.25) equal to 41.098205557 and -41.098205557.Subproblem 1
x + -46.25 = 41.098205557 Simplifying x + -46.25 = 41.098205557 Reorder the terms: -46.25 + x = 41.098205557 Solving -46.25 + x = 41.098205557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46.25' to each side of the equation. -46.25 + 46.25 + x = 41.098205557 + 46.25 Combine like terms: -46.25 + 46.25 = 0.00 0.00 + x = 41.098205557 + 46.25 x = 41.098205557 + 46.25 Combine like terms: 41.098205557 + 46.25 = 87.348205557 x = 87.348205557 Simplifying x = 87.348205557Subproblem 2
x + -46.25 = -41.098205557 Simplifying x + -46.25 = -41.098205557 Reorder the terms: -46.25 + x = -41.098205557 Solving -46.25 + x = -41.098205557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46.25' to each side of the equation. -46.25 + 46.25 + x = -41.098205557 + 46.25 Combine like terms: -46.25 + 46.25 = 0.00 0.00 + x = -41.098205557 + 46.25 x = -41.098205557 + 46.25 Combine like terms: -41.098205557 + 46.25 = 5.151794443 x = 5.151794443 Simplifying x = 5.151794443Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.348205557, 5.151794443}Solution
x = {87.348205557, 5.151794443}
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