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Simplifying 4000 = 2x2 + 18x Reorder the terms: 4000 = 18x + 2x2 Solving 4000 = 18x + 2x2 Solving for variable 'x'. Reorder the terms: 4000 + -18x + -2x2 = 18x + -18x + 2x2 + -2x2 Combine like terms: 18x + -18x = 0 4000 + -18x + -2x2 = 0 + 2x2 + -2x2 4000 + -18x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 4000 + -18x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2000 + -9x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2000 + -9x + -1x2)' equal to zero and attempt to solve: Simplifying 2000 + -9x + -1x2 = 0 Solving 2000 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2000 + 9x + x2 = 0 Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 9x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 9x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 9x + x2 = 0 + 2000 9x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 9x + x2 = 2000 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 2000 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 2000 + 20.25 Combine like terms: 2000 + 20.25 = 2020.25 20.25 + 9x + x2 = 2020.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 2020.25 Calculate the square root of the right side: 44.947191236 Break this problem into two subproblems by setting (x + 4.5) equal to 44.947191236 and -44.947191236.Subproblem 1
x + 4.5 = 44.947191236 Simplifying x + 4.5 = 44.947191236 Reorder the terms: 4.5 + x = 44.947191236 Solving 4.5 + x = 44.947191236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 44.947191236 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 44.947191236 + -4.5 x = 44.947191236 + -4.5 Combine like terms: 44.947191236 + -4.5 = 40.447191236 x = 40.447191236 Simplifying x = 40.447191236Subproblem 2
x + 4.5 = -44.947191236 Simplifying x + 4.5 = -44.947191236 Reorder the terms: 4.5 + x = -44.947191236 Solving 4.5 + x = -44.947191236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -44.947191236 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -44.947191236 + -4.5 x = -44.947191236 + -4.5 Combine like terms: -44.947191236 + -4.5 = -49.447191236 x = -49.447191236 Simplifying x = -49.447191236Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.447191236, -49.447191236}Solution
x = {40.447191236, -49.447191236}
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