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Simplifying 12300 = -143.3x2 + 1823.3x + 6820 Reorder the terms: 12300 = 6820 + 1823.3x + -143.3x2 Solving 12300 = 6820 + 1823.3x + -143.3x2 Solving for variable 'x'. Combine like terms: 12300 + -6820 = 5480 5480 + -1823.3x + 143.3x2 = 6820 + 1823.3x + -143.3x2 + -6820 + -1823.3x + 143.3x2 Reorder the terms: 5480 + -1823.3x + 143.3x2 = 6820 + -6820 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 6820 + -6820 = 0 5480 + -1823.3x + 143.3x2 = 0 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 5480 + -1823.3x + 143.3x2 = 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 1823.3x + -1823.3x = 0.0 5480 + -1823.3x + 143.3x2 = 0.0 + -143.3x2 + 143.3x2 5480 + -1823.3x + 143.3x2 = -143.3x2 + 143.3x2 Combine like terms: -143.3x2 + 143.3x2 = 0.0 5480 + -1823.3x + 143.3x2 = 0.0 Begin completing the square. Divide all terms by 143.3 the coefficient of the squared term: Divide each side by '143.3'. 38.2414515 + -12.72365666x + x2 = 0 Move the constant term to the right: Add '-38.2414515' to each side of the equation. 38.2414515 + -12.72365666x + -38.2414515 + x2 = 0 + -38.2414515 Reorder the terms: 38.2414515 + -38.2414515 + -12.72365666x + x2 = 0 + -38.2414515 Combine like terms: 38.2414515 + -38.2414515 = 0.0000000 0.0000000 + -12.72365666x + x2 = 0 + -38.2414515 -12.72365666x + x2 = 0 + -38.2414515 Combine like terms: 0 + -38.2414515 = -38.2414515 -12.72365666x + x2 = -38.2414515 The x term is -12.72365666x. Take half its coefficient (-6.36182833). Square it (40.47285970) and add it to both sides. Add '40.47285970' to each side of the equation. -12.72365666x + 40.47285970 + x2 = -38.2414515 + 40.47285970 Reorder the terms: 40.47285970 + -12.72365666x + x2 = -38.2414515 + 40.47285970 Combine like terms: -38.2414515 + 40.47285970 = 2.2314082 40.47285970 + -12.72365666x + x2 = 2.2314082 Factor a perfect square on the left side: (x + -6.36182833)(x + -6.36182833) = 2.2314082 Calculate the square root of the right side: 1.493789878 Break this problem into two subproblems by setting (x + -6.36182833) equal to 1.493789878 and -1.493789878.Subproblem 1
x + -6.36182833 = 1.493789878 Simplifying x + -6.36182833 = 1.493789878 Reorder the terms: -6.36182833 + x = 1.493789878 Solving -6.36182833 + x = 1.493789878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.36182833' to each side of the equation. -6.36182833 + 6.36182833 + x = 1.493789878 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = 1.493789878 + 6.36182833 x = 1.493789878 + 6.36182833 Combine like terms: 1.493789878 + 6.36182833 = 7.855618208 x = 7.855618208 Simplifying x = 7.855618208Subproblem 2
x + -6.36182833 = -1.493789878 Simplifying x + -6.36182833 = -1.493789878 Reorder the terms: -6.36182833 + x = -1.493789878 Solving -6.36182833 + x = -1.493789878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.36182833' to each side of the equation. -6.36182833 + 6.36182833 + x = -1.493789878 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = -1.493789878 + 6.36182833 x = -1.493789878 + 6.36182833 Combine like terms: -1.493789878 + 6.36182833 = 4.868038452 x = 4.868038452 Simplifying x = 4.868038452Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.855618208, 4.868038452}
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