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Simplifying 30x2 + -77x + -60 = 0 Reorder the terms: -60 + -77x + 30x2 = 0 Solving -60 + -77x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -2 + -2.566666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.566666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2.566666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.566666667x + x2 = 0 + 2 -2.566666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.566666667x + x2 = 2 The x term is -2.566666667x. Take half its coefficient (-1.283333334). Square it (1.646944446) and add it to both sides. Add '1.646944446' to each side of the equation. -2.566666667x + 1.646944446 + x2 = 2 + 1.646944446 Reorder the terms: 1.646944446 + -2.566666667x + x2 = 2 + 1.646944446 Combine like terms: 2 + 1.646944446 = 3.646944446 1.646944446 + -2.566666667x + x2 = 3.646944446 Factor a perfect square on the left side: (x + -1.283333334)(x + -1.283333334) = 3.646944446 Calculate the square root of the right side: 1.909697475 Break this problem into two subproblems by setting (x + -1.283333334) equal to 1.909697475 and -1.909697475.Subproblem 1
x + -1.283333334 = 1.909697475 Simplifying x + -1.283333334 = 1.909697475 Reorder the terms: -1.283333334 + x = 1.909697475 Solving -1.283333334 + x = 1.909697475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.283333334' to each side of the equation. -1.283333334 + 1.283333334 + x = 1.909697475 + 1.283333334 Combine like terms: -1.283333334 + 1.283333334 = 0.000000000 0.000000000 + x = 1.909697475 + 1.283333334 x = 1.909697475 + 1.283333334 Combine like terms: 1.909697475 + 1.283333334 = 3.193030809 x = 3.193030809 Simplifying x = 3.193030809Subproblem 2
x + -1.283333334 = -1.909697475 Simplifying x + -1.283333334 = -1.909697475 Reorder the terms: -1.283333334 + x = -1.909697475 Solving -1.283333334 + x = -1.909697475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.283333334' to each side of the equation. -1.283333334 + 1.283333334 + x = -1.909697475 + 1.283333334 Combine like terms: -1.283333334 + 1.283333334 = 0.000000000 0.000000000 + x = -1.909697475 + 1.283333334 x = -1.909697475 + 1.283333334 Combine like terms: -1.909697475 + 1.283333334 = -0.626364141 x = -0.626364141 Simplifying x = -0.626364141Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.193030809, -0.626364141}
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