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Simplifying 2x2 + 74x + -1800 = 0 Reorder the terms: -1800 + 74x + 2x2 = 0 Solving -1800 + 74x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-900 + 37x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-900 + 37x + x2)' equal to zero and attempt to solve: Simplifying -900 + 37x + x2 = 0 Solving -900 + 37x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + 37x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 37x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 37x + x2 = 0 + 900 37x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 37x + x2 = 900 The x term is 37x. Take half its coefficient (18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. 37x + 342.25 + x2 = 900 + 342.25 Reorder the terms: 342.25 + 37x + x2 = 900 + 342.25 Combine like terms: 900 + 342.25 = 1242.25 342.25 + 37x + x2 = 1242.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 1242.25 Calculate the square root of the right side: 35.245567097 Break this problem into two subproblems by setting (x + 18.5) equal to 35.245567097 and -35.245567097.Subproblem 1
x + 18.5 = 35.245567097 Simplifying x + 18.5 = 35.245567097 Reorder the terms: 18.5 + x = 35.245567097 Solving 18.5 + x = 35.245567097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = 35.245567097 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 35.245567097 + -18.5 x = 35.245567097 + -18.5 Combine like terms: 35.245567097 + -18.5 = 16.745567097 x = 16.745567097 Simplifying x = 16.745567097Subproblem 2
x + 18.5 = -35.245567097 Simplifying x + 18.5 = -35.245567097 Reorder the terms: 18.5 + x = -35.245567097 Solving 18.5 + x = -35.245567097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = -35.245567097 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -35.245567097 + -18.5 x = -35.245567097 + -18.5 Combine like terms: -35.245567097 + -18.5 = -53.745567097 x = -53.745567097 Simplifying x = -53.745567097Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.745567097, -53.745567097}Solution
x = {16.745567097, -53.745567097}
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