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Simplifying 9x2 + -102x + 252 = 0 Reorder the terms: 252 + -102x + 9x2 = 0 Solving 252 + -102x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(84 + -34x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(84 + -34x + 3x2)' equal to zero and attempt to solve: Simplifying 84 + -34x + 3x2 = 0 Solving 84 + -34x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 28 + -11.33333333x + x2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + -11.33333333x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -11.33333333x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -11.33333333x + x2 = 0 + -28 -11.33333333x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -11.33333333x + x2 = -28 The x term is -11.33333333x. Take half its coefficient (-5.666666665). Square it (32.11111109) and add it to both sides. Add '32.11111109' to each side of the equation. -11.33333333x + 32.11111109 + x2 = -28 + 32.11111109 Reorder the terms: 32.11111109 + -11.33333333x + x2 = -28 + 32.11111109 Combine like terms: -28 + 32.11111109 = 4.11111109 32.11111109 + -11.33333333x + x2 = 4.11111109 Factor a perfect square on the left side: (x + -5.666666665)(x + -5.666666665) = 4.11111109 Calculate the square root of the right side: 2.027587505 Break this problem into two subproblems by setting (x + -5.666666665) equal to 2.027587505 and -2.027587505.Subproblem 1
x + -5.666666665 = 2.027587505 Simplifying x + -5.666666665 = 2.027587505 Reorder the terms: -5.666666665 + x = 2.027587505 Solving -5.666666665 + x = 2.027587505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = 2.027587505 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = 2.027587505 + 5.666666665 x = 2.027587505 + 5.666666665 Combine like terms: 2.027587505 + 5.666666665 = 7.69425417 x = 7.69425417 Simplifying x = 7.69425417Subproblem 2
x + -5.666666665 = -2.027587505 Simplifying x + -5.666666665 = -2.027587505 Reorder the terms: -5.666666665 + x = -2.027587505 Solving -5.666666665 + x = -2.027587505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = -2.027587505 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = -2.027587505 + 5.666666665 x = -2.027587505 + 5.666666665 Combine like terms: -2.027587505 + 5.666666665 = 3.63907916 x = 3.63907916 Simplifying x = 3.63907916Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.69425417, 3.63907916}Solution
x = {7.69425417, 3.63907916}
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