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Simplifying 600 = -15x2 + 330x + -1150 Reorder the terms: 600 = -1150 + 330x + -15x2 Solving 600 = -1150 + 330x + -15x2 Solving for variable 'x'. Combine like terms: 600 + 1150 = 1750 1750 + -330x + 15x2 = -1150 + 330x + -15x2 + 1150 + -330x + 15x2 Reorder the terms: 1750 + -330x + 15x2 = -1150 + 1150 + 330x + -330x + -15x2 + 15x2 Combine like terms: -1150 + 1150 = 0 1750 + -330x + 15x2 = 0 + 330x + -330x + -15x2 + 15x2 1750 + -330x + 15x2 = 330x + -330x + -15x2 + 15x2 Combine like terms: 330x + -330x = 0 1750 + -330x + 15x2 = 0 + -15x2 + 15x2 1750 + -330x + 15x2 = -15x2 + 15x2 Combine like terms: -15x2 + 15x2 = 0 1750 + -330x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(350 + -66x + 3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(350 + -66x + 3x2)' equal to zero and attempt to solve: Simplifying 350 + -66x + 3x2 = 0 Solving 350 + -66x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 116.6666667 + -22x + x2 = 0 Move the constant term to the right: Add '-116.6666667' to each side of the equation. 116.6666667 + -22x + -116.6666667 + x2 = 0 + -116.6666667 Reorder the terms: 116.6666667 + -116.6666667 + -22x + x2 = 0 + -116.6666667 Combine like terms: 116.6666667 + -116.6666667 = 0.0000000 0.0000000 + -22x + x2 = 0 + -116.6666667 -22x + x2 = 0 + -116.6666667 Combine like terms: 0 + -116.6666667 = -116.6666667 -22x + x2 = -116.6666667 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 = -116.6666667 + 121 Reorder the terms: 121 + -22x + x2 = -116.6666667 + 121 Combine like terms: -116.6666667 + 121 = 4.3333333 121 + -22x + x2 = 4.3333333 Factor a perfect square on the left side: (x + -11)(x + -11) = 4.3333333 Calculate the square root of the right side: 2.081665991 Break this problem into two subproblems by setting (x + -11) equal to 2.081665991 and -2.081665991.Subproblem 1
x + -11 = 2.081665991 Simplifying x + -11 = 2.081665991 Reorder the terms: -11 + x = 2.081665991 Solving -11 + x = 2.081665991 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 = 2.081665991 + 11 Combine like terms: -11 + 11 = 0 0 + x = 2.081665991 + 11 x = 2.081665991 + 11 Combine like terms: 2.081665991 + 11 = 13.081665991 x = 13.081665991 Simplifying x = 13.081665991Subproblem 2
x + -11 = -2.081665991 Simplifying x + -11 = -2.081665991 Reorder the terms: -11 + x = -2.081665991 Solving -11 + x = -2.081665991 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 = -2.081665991 + 11 Combine like terms: -11 + 11 = 0 0 + x = -2.081665991 + 11 x = -2.081665991 + 11 Combine like terms: -2.081665991 + 11 = 8.918334009 x = 8.918334009 Simplifying x = 8.918334009Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.081665991, 8.918334009}Solution
x = {13.081665991, 8.918334009}
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