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Simplifying -45x2 + 990x + 15570 = 21000 Reorder the terms: 15570 + 990x + -45x2 = 21000 Solving 15570 + 990x + -45x2 = 21000 Solving for variable 'x'. Reorder the terms: 15570 + -21000 + 990x + -45x2 = 21000 + -21000 Combine like terms: 15570 + -21000 = -5430 -5430 + 990x + -45x2 = 21000 + -21000 Combine like terms: 21000 + -21000 = 0 -5430 + 990x + -45x2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-362 + 66x + -3x2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-362 + 66x + -3x2)' equal to zero and attempt to solve: Simplifying -362 + 66x + -3x2 = 0 Solving -362 + 66x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 120.6666667 + -22x + x2 = 0 Move the constant term to the right: Add '-120.6666667' to each side of the equation. 120.6666667 + -22x + -120.6666667 + x2 = 0 + -120.6666667 Reorder the terms: 120.6666667 + -120.6666667 + -22x + x2 = 0 + -120.6666667 Combine like terms: 120.6666667 + -120.6666667 = 0.0000000 0.0000000 + -22x + x2 = 0 + -120.6666667 -22x + x2 = 0 + -120.6666667 Combine like terms: 0 + -120.6666667 = -120.6666667 -22x + x2 = -120.6666667 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -120.6666667 + 121 Reorder the terms: 121 + -22x + x2 = -120.6666667 + 121 Combine like terms: -120.6666667 + 121 = 0.3333333 121 + -22x + x2 = 0.3333333 Factor a perfect square on the left side: (x + -11)(x + -11) = 0.3333333 Calculate the square root of the right side: 0.57735024 Break this problem into two subproblems by setting (x + -11) equal to 0.57735024 and -0.57735024.Subproblem 1
x + -11 = 0.57735024 Simplifying x + -11 = 0.57735024 Reorder the terms: -11 + x = 0.57735024 Solving -11 + x = 0.57735024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 0.57735024 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0.57735024 + 11 x = 0.57735024 + 11 Combine like terms: 0.57735024 + 11 = 11.57735024 x = 11.57735024 Simplifying x = 11.57735024Subproblem 2
x + -11 = -0.57735024 Simplifying x + -11 = -0.57735024 Reorder the terms: -11 + x = -0.57735024 Solving -11 + x = -0.57735024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -0.57735024 + 11 Combine like terms: -11 + 11 = 0 0 + x = -0.57735024 + 11 x = -0.57735024 + 11 Combine like terms: -0.57735024 + 11 = 10.42264976 x = 10.42264976 Simplifying x = 10.42264976Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.57735024, 10.42264976}Solution
x = {11.57735024, 10.42264976}
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