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Simplifying 7 = -143.3x2 + 1823.3x + 6820 Reorder the terms: 7 = 6820 + 1823.3x + -143.3x2 Solving 7 = 6820 + 1823.3x + -143.3x2 Solving for variable 'x'. Combine like terms: 7 + -6820 = -6813 -6813 + -1823.3x + 143.3x2 = 6820 + 1823.3x + -143.3x2 + -6820 + -1823.3x + 143.3x2 Reorder the terms: -6813 + -1823.3x + 143.3x2 = 6820 + -6820 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 6820 + -6820 = 0 -6813 + -1823.3x + 143.3x2 = 0 + 1823.3x + -1823.3x + -143.3x2 + 143.3x2 -6813 + -1823.3x + 143.3x2 = 1823.3x + -1823.3x + -143.3x2 + 143.3x2 Combine like terms: 1823.3x + -1823.3x = 0.0 -6813 + -1823.3x + 143.3x2 = 0.0 + -143.3x2 + 143.3x2 -6813 + -1823.3x + 143.3x2 = -143.3x2 + 143.3x2 Combine like terms: -143.3x2 + 143.3x2 = 0.0 -6813 + -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'. -47.54361479 + -12.72365666x + x2 = 0 Move the constant term to the right: Add '47.54361479' to each side of the equation. -47.54361479 + -12.72365666x + 47.54361479 + x2 = 0 + 47.54361479 Reorder the terms: -47.54361479 + 47.54361479 + -12.72365666x + x2 = 0 + 47.54361479 Combine like terms: -47.54361479 + 47.54361479 = 0.00000000 0.00000000 + -12.72365666x + x2 = 0 + 47.54361479 -12.72365666x + x2 = 0 + 47.54361479 Combine like terms: 0 + 47.54361479 = 47.54361479 -12.72365666x + x2 = 47.54361479 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 = 47.54361479 + 40.47285970 Reorder the terms: 40.47285970 + -12.72365666x + x2 = 47.54361479 + 40.47285970 Combine like terms: 47.54361479 + 40.47285970 = 88.01647449 40.47285970 + -12.72365666x + x2 = 88.01647449 Factor a perfect square on the left side: (x + -6.36182833)(x + -6.36182833) = 88.01647449 Calculate the square root of the right side: 9.381709572 Break this problem into two subproblems by setting (x + -6.36182833) equal to 9.381709572 and -9.381709572.Subproblem 1
x + -6.36182833 = 9.381709572 Simplifying x + -6.36182833 = 9.381709572 Reorder the terms: -6.36182833 + x = 9.381709572 Solving -6.36182833 + x = 9.381709572 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 = 9.381709572 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = 9.381709572 + 6.36182833 x = 9.381709572 + 6.36182833 Combine like terms: 9.381709572 + 6.36182833 = 15.743537902 x = 15.743537902 Simplifying x = 15.743537902Subproblem 2
x + -6.36182833 = -9.381709572 Simplifying x + -6.36182833 = -9.381709572 Reorder the terms: -6.36182833 + x = -9.381709572 Solving -6.36182833 + x = -9.381709572 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 = -9.381709572 + 6.36182833 Combine like terms: -6.36182833 + 6.36182833 = 0.00000000 0.00000000 + x = -9.381709572 + 6.36182833 x = -9.381709572 + 6.36182833 Combine like terms: -9.381709572 + 6.36182833 = -3.019881242 x = -3.019881242 Simplifying x = -3.019881242Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.743537902, -3.019881242}
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