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Simplifying x(33600x + -177200) = 288400 Reorder the terms: x(-177200 + 33600x) = 288400 (-177200 * x + 33600x * x) = 288400 (-177200x + 33600x2) = 288400 Solving -177200x + 33600x2 = 288400 Solving for variable 'x'. Reorder the terms: -288400 + -177200x + 33600x2 = 288400 + -288400 Combine like terms: 288400 + -288400 = 0 -288400 + -177200x + 33600x2 = 0 Factor out the Greatest Common Factor (GCF), '400'. 400(-721 + -443x + 84x2) = 0 Ignore the factor 400.Subproblem 1
Set the factor '(-721 + -443x + 84x2)' equal to zero and attempt to solve: Simplifying -721 + -443x + 84x2 = 0 Solving -721 + -443x + 84x2 = 0 Begin completing the square. Divide all terms by 84 the coefficient of the squared term: Divide each side by '84'. -8.583333333 + -5.273809524x + x2 = 0 Move the constant term to the right: Add '8.583333333' to each side of the equation. -8.583333333 + -5.273809524x + 8.583333333 + x2 = 0 + 8.583333333 Reorder the terms: -8.583333333 + 8.583333333 + -5.273809524x + x2 = 0 + 8.583333333 Combine like terms: -8.583333333 + 8.583333333 = 0.000000000 0.000000000 + -5.273809524x + x2 = 0 + 8.583333333 -5.273809524x + x2 = 0 + 8.583333333 Combine like terms: 0 + 8.583333333 = 8.583333333 -5.273809524x + x2 = 8.583333333 The x term is -5.273809524x. Take half its coefficient (-2.636904762). Square it (6.953266724) and add it to both sides. Add '6.953266724' to each side of the equation. -5.273809524x + 6.953266724 + x2 = 8.583333333 + 6.953266724 Reorder the terms: 6.953266724 + -5.273809524x + x2 = 8.583333333 + 6.953266724 Combine like terms: 8.583333333 + 6.953266724 = 15.536600057 6.953266724 + -5.273809524x + x2 = 15.536600057 Factor a perfect square on the left side: (x + -2.636904762)(x + -2.636904762) = 15.536600057 Calculate the square root of the right side: 3.941649408 Break this problem into two subproblems by setting (x + -2.636904762) equal to 3.941649408 and -3.941649408.Subproblem 1
x + -2.636904762 = 3.941649408 Simplifying x + -2.636904762 = 3.941649408 Reorder the terms: -2.636904762 + x = 3.941649408 Solving -2.636904762 + x = 3.941649408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.636904762' to each side of the equation. -2.636904762 + 2.636904762 + x = 3.941649408 + 2.636904762 Combine like terms: -2.636904762 + 2.636904762 = 0.000000000 0.000000000 + x = 3.941649408 + 2.636904762 x = 3.941649408 + 2.636904762 Combine like terms: 3.941649408 + 2.636904762 = 6.57855417 x = 6.57855417 Simplifying x = 6.57855417Subproblem 2
x + -2.636904762 = -3.941649408 Simplifying x + -2.636904762 = -3.941649408 Reorder the terms: -2.636904762 + x = -3.941649408 Solving -2.636904762 + x = -3.941649408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.636904762' to each side of the equation. -2.636904762 + 2.636904762 + x = -3.941649408 + 2.636904762 Combine like terms: -2.636904762 + 2.636904762 = 0.000000000 0.000000000 + x = -3.941649408 + 2.636904762 x = -3.941649408 + 2.636904762 Combine like terms: -3.941649408 + 2.636904762 = -1.304744646 x = -1.304744646 Simplifying x = -1.304744646Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.57855417, -1.304744646}Solution
x = {6.57855417, -1.304744646}
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