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Simplifying 3x2 + -52x + 144 = 0 Reorder the terms: 144 + -52x + 3x2 = 0 Solving 144 + -52x + 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'. 48 + -17.33333333x + x2 = 0 Move the constant term to the right: Add '-48' to each side of the equation. 48 + -17.33333333x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + -17.33333333x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -17.33333333x + x2 = 0 + -48 -17.33333333x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -17.33333333x + x2 = -48 The x term is -17.33333333x. Take half its coefficient (-8.666666665). Square it (75.11111108) and add it to both sides. Add '75.11111108' to each side of the equation. -17.33333333x + 75.11111108 + x2 = -48 + 75.11111108 Reorder the terms: 75.11111108 + -17.33333333x + x2 = -48 + 75.11111108 Combine like terms: -48 + 75.11111108 = 27.11111108 75.11111108 + -17.33333333x + x2 = 27.11111108 Factor a perfect square on the left side: (x + -8.666666665)(x + -8.666666665) = 27.11111108 Calculate the square root of the right side: 5.206833114 Break this problem into two subproblems by setting (x + -8.666666665) equal to 5.206833114 and -5.206833114.Subproblem 1
x + -8.666666665 = 5.206833114 Simplifying x + -8.666666665 = 5.206833114 Reorder the terms: -8.666666665 + x = 5.206833114 Solving -8.666666665 + x = 5.206833114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.666666665' to each side of the equation. -8.666666665 + 8.666666665 + x = 5.206833114 + 8.666666665 Combine like terms: -8.666666665 + 8.666666665 = 0.000000000 0.000000000 + x = 5.206833114 + 8.666666665 x = 5.206833114 + 8.666666665 Combine like terms: 5.206833114 + 8.666666665 = 13.873499779 x = 13.873499779 Simplifying x = 13.873499779Subproblem 2
x + -8.666666665 = -5.206833114 Simplifying x + -8.666666665 = -5.206833114 Reorder the terms: -8.666666665 + x = -5.206833114 Solving -8.666666665 + x = -5.206833114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.666666665' to each side of the equation. -8.666666665 + 8.666666665 + x = -5.206833114 + 8.666666665 Combine like terms: -8.666666665 + 8.666666665 = 0.000000000 0.000000000 + x = -5.206833114 + 8.666666665 x = -5.206833114 + 8.666666665 Combine like terms: -5.206833114 + 8.666666665 = 3.459833551 x = 3.459833551 Simplifying x = 3.459833551Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.873499779, 3.459833551}
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