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Simplifying 3x2 + 5x + -2200 = 0 Reorder the terms: -2200 + 5x + 3x2 = 0 Solving -2200 + 5x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -733.3333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '733.3333333' to each side of the equation. -733.3333333 + 1.666666667x + 733.3333333 + x2 = 0 + 733.3333333 Reorder the terms: -733.3333333 + 733.3333333 + 1.666666667x + x2 = 0 + 733.3333333 Combine like terms: -733.3333333 + 733.3333333 = 0.0000000 0.0000000 + 1.666666667x + x2 = 0 + 733.3333333 1.666666667x + x2 = 0 + 733.3333333 Combine like terms: 0 + 733.3333333 = 733.3333333 1.666666667x + x2 = 733.3333333 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 733.3333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 733.3333333 + 0.6944444447 Combine like terms: 733.3333333 + 0.6944444447 = 734.0277777447 0.6944444447 + 1.666666667x + x2 = 734.0277777447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 734.0277777447 Calculate the square root of the right side: 27.092947011 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 27.092947011 and -27.092947011.Subproblem 1
x + 0.8333333335 = 27.092947011 Simplifying x + 0.8333333335 = 27.092947011 Reorder the terms: 0.8333333335 + x = 27.092947011 Solving 0.8333333335 + x = 27.092947011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 27.092947011 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 27.092947011 + -0.8333333335 x = 27.092947011 + -0.8333333335 Combine like terms: 27.092947011 + -0.8333333335 = 26.2596136775 x = 26.2596136775 Simplifying x = 26.2596136775Subproblem 2
x + 0.8333333335 = -27.092947011 Simplifying x + 0.8333333335 = -27.092947011 Reorder the terms: 0.8333333335 + x = -27.092947011 Solving 0.8333333335 + x = -27.092947011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -27.092947011 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -27.092947011 + -0.8333333335 x = -27.092947011 + -0.8333333335 Combine like terms: -27.092947011 + -0.8333333335 = -27.9262803445 x = -27.9262803445 Simplifying x = -27.9262803445Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.2596136775, -27.9262803445}
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