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Simplifying 3900x + 2300x2 = 8700 Solving 3900x + 2300x2 = 8700 Solving for variable 'x'. Reorder the terms: -8700 + 3900x + 2300x2 = 8700 + -8700 Combine like terms: 8700 + -8700 = 0 -8700 + 3900x + 2300x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(-87 + 39x + 23x2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(-87 + 39x + 23x2)' equal to zero and attempt to solve: Simplifying -87 + 39x + 23x2 = 0 Solving -87 + 39x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -3.782608696 + 1.695652174x + x2 = 0 Move the constant term to the right: Add '3.782608696' to each side of the equation. -3.782608696 + 1.695652174x + 3.782608696 + x2 = 0 + 3.782608696 Reorder the terms: -3.782608696 + 3.782608696 + 1.695652174x + x2 = 0 + 3.782608696 Combine like terms: -3.782608696 + 3.782608696 = 0.000000000 0.000000000 + 1.695652174x + x2 = 0 + 3.782608696 1.695652174x + x2 = 0 + 3.782608696 Combine like terms: 0 + 3.782608696 = 3.782608696 1.695652174x + x2 = 3.782608696 The x term is 1.695652174x. Take half its coefficient (0.847826087). Square it (0.7188090738) and add it to both sides. Add '0.7188090738' to each side of the equation. 1.695652174x + 0.7188090738 + x2 = 3.782608696 + 0.7188090738 Reorder the terms: 0.7188090738 + 1.695652174x + x2 = 3.782608696 + 0.7188090738 Combine like terms: 3.782608696 + 0.7188090738 = 4.5014177698 0.7188090738 + 1.695652174x + x2 = 4.5014177698 Factor a perfect square on the left side: (x + 0.847826087)(x + 0.847826087) = 4.5014177698 Calculate the square root of the right side: 2.121654489 Break this problem into two subproblems by setting (x + 0.847826087) equal to 2.121654489 and -2.121654489.Subproblem 1
x + 0.847826087 = 2.121654489 Simplifying x + 0.847826087 = 2.121654489 Reorder the terms: 0.847826087 + x = 2.121654489 Solving 0.847826087 + x = 2.121654489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.847826087' to each side of the equation. 0.847826087 + -0.847826087 + x = 2.121654489 + -0.847826087 Combine like terms: 0.847826087 + -0.847826087 = 0.000000000 0.000000000 + x = 2.121654489 + -0.847826087 x = 2.121654489 + -0.847826087 Combine like terms: 2.121654489 + -0.847826087 = 1.273828402 x = 1.273828402 Simplifying x = 1.273828402Subproblem 2
x + 0.847826087 = -2.121654489 Simplifying x + 0.847826087 = -2.121654489 Reorder the terms: 0.847826087 + x = -2.121654489 Solving 0.847826087 + x = -2.121654489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.847826087' to each side of the equation. 0.847826087 + -0.847826087 + x = -2.121654489 + -0.847826087 Combine like terms: 0.847826087 + -0.847826087 = 0.000000000 0.000000000 + x = -2.121654489 + -0.847826087 x = -2.121654489 + -0.847826087 Combine like terms: -2.121654489 + -0.847826087 = -2.969480576 x = -2.969480576 Simplifying x = -2.969480576Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.273828402, -2.969480576}Solution
x = {1.273828402, -2.969480576}
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