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Simplifying 12x2 + -13x + -72 = 0 Reorder the terms: -72 + -13x + 12x2 = 0 Solving -72 + -13x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -6 + -1.083333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.083333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -1.083333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.083333333x + x2 = 0 + 6 -1.083333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.083333333x + x2 = 6 The x term is -1.083333333x. Take half its coefficient (-0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. -1.083333333x + 0.2934027776 + x2 = 6 + 0.2934027776 Reorder the terms: 0.2934027776 + -1.083333333x + x2 = 6 + 0.2934027776 Combine like terms: 6 + 0.2934027776 = 6.2934027776 0.2934027776 + -1.083333333x + x2 = 6.2934027776 Factor a perfect square on the left side: (x + -0.5416666665)(x + -0.5416666665) = 6.2934027776 Calculate the square root of the right side: 2.508665537 Break this problem into two subproblems by setting (x + -0.5416666665) equal to 2.508665537 and -2.508665537.Subproblem 1
x + -0.5416666665 = 2.508665537 Simplifying x + -0.5416666665 = 2.508665537 Reorder the terms: -0.5416666665 + x = 2.508665537 Solving -0.5416666665 + x = 2.508665537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + x = 2.508665537 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = 2.508665537 + 0.5416666665 x = 2.508665537 + 0.5416666665 Combine like terms: 2.508665537 + 0.5416666665 = 3.0503322035 x = 3.0503322035 Simplifying x = 3.0503322035Subproblem 2
x + -0.5416666665 = -2.508665537 Simplifying x + -0.5416666665 = -2.508665537 Reorder the terms: -0.5416666665 + x = -2.508665537 Solving -0.5416666665 + x = -2.508665537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + x = -2.508665537 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = -2.508665537 + 0.5416666665 x = -2.508665537 + 0.5416666665 Combine like terms: -2.508665537 + 0.5416666665 = -1.9669988705 x = -1.9669988705 Simplifying x = -1.9669988705Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0503322035, -1.9669988705}
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