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Simplifying 600 = -15x2 + 330x + -815 Reorder the terms: 600 = -815 + 330x + -15x2 Solving 600 = -815 + 330x + -15x2 Solving for variable 'x'. Combine like terms: 600 + 815 = 1415 1415 + -330x + 15x2 = -815 + 330x + -15x2 + 815 + -330x + 15x2 Reorder the terms: 1415 + -330x + 15x2 = -815 + 815 + 330x + -330x + -15x2 + 15x2 Combine like terms: -815 + 815 = 0 1415 + -330x + 15x2 = 0 + 330x + -330x + -15x2 + 15x2 1415 + -330x + 15x2 = 330x + -330x + -15x2 + 15x2 Combine like terms: 330x + -330x = 0 1415 + -330x + 15x2 = 0 + -15x2 + 15x2 1415 + -330x + 15x2 = -15x2 + 15x2 Combine like terms: -15x2 + 15x2 = 0 1415 + -330x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(283 + -66x + 3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(283 + -66x + 3x2)' equal to zero and attempt to solve: Simplifying 283 + -66x + 3x2 = 0 Solving 283 + -66x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 94.33333333 + -22x + x2 = 0 Move the constant term to the right: Add '-94.33333333' to each side of the equation. 94.33333333 + -22x + -94.33333333 + x2 = 0 + -94.33333333 Reorder the terms: 94.33333333 + -94.33333333 + -22x + x2 = 0 + -94.33333333 Combine like terms: 94.33333333 + -94.33333333 = 0.00000000 0.00000000 + -22x + x2 = 0 + -94.33333333 -22x + x2 = 0 + -94.33333333 Combine like terms: 0 + -94.33333333 = -94.33333333 -22x + x2 = -94.33333333 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 = -94.33333333 + 121 Reorder the terms: 121 + -22x + x2 = -94.33333333 + 121 Combine like terms: -94.33333333 + 121 = 26.66666667 121 + -22x + x2 = 26.66666667 Factor a perfect square on the left side: (x + -11)(x + -11) = 26.66666667 Calculate the square root of the right side: 5.163977795 Break this problem into two subproblems by setting (x + -11) equal to 5.163977795 and -5.163977795.Subproblem 1
x + -11 = 5.163977795 Simplifying x + -11 = 5.163977795 Reorder the terms: -11 + x = 5.163977795 Solving -11 + x = 5.163977795 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 = 5.163977795 + 11 Combine like terms: -11 + 11 = 0 0 + x = 5.163977795 + 11 x = 5.163977795 + 11 Combine like terms: 5.163977795 + 11 = 16.163977795 x = 16.163977795 Simplifying x = 16.163977795Subproblem 2
x + -11 = -5.163977795 Simplifying x + -11 = -5.163977795 Reorder the terms: -11 + x = -5.163977795 Solving -11 + x = -5.163977795 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 = -5.163977795 + 11 Combine like terms: -11 + 11 = 0 0 + x = -5.163977795 + 11 x = -5.163977795 + 11 Combine like terms: -5.163977795 + 11 = 5.836022205 x = 5.836022205 Simplifying x = 5.836022205Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.163977795, 5.836022205}Solution
x = {16.163977795, 5.836022205}
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