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Simplifying 12x2 + -7x + -20 = 0 Reorder the terms: -20 + -7x + 12x2 = 0 Solving -20 + -7x + 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'. -1.666666667 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -0.5833333333x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -0.5833333333x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -0.5833333333x + x2 = 0 + 1.666666667 -0.5833333333x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -0.5833333333x + x2 = 1.666666667 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 1.666666667 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 1.666666667 + 0.08506944446 Combine like terms: 1.666666667 + 0.08506944446 = 1.75173611146 0.08506944446 + -0.5833333333x + x2 = 1.75173611146 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 1.75173611146 Calculate the square root of the right side: 1.323531681 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 1.323531681 and -1.323531681.Subproblem 1
x + -0.2916666667 = 1.323531681 Simplifying x + -0.2916666667 = 1.323531681 Reorder the terms: -0.2916666667 + x = 1.323531681 Solving -0.2916666667 + x = 1.323531681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 1.323531681 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 1.323531681 + 0.2916666667 x = 1.323531681 + 0.2916666667 Combine like terms: 1.323531681 + 0.2916666667 = 1.6151983477 x = 1.6151983477 Simplifying x = 1.6151983477Subproblem 2
x + -0.2916666667 = -1.323531681 Simplifying x + -0.2916666667 = -1.323531681 Reorder the terms: -0.2916666667 + x = -1.323531681 Solving -0.2916666667 + x = -1.323531681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -1.323531681 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -1.323531681 + 0.2916666667 x = -1.323531681 + 0.2916666667 Combine like terms: -1.323531681 + 0.2916666667 = -1.0318650143 x = -1.0318650143 Simplifying x = -1.0318650143Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6151983477, -1.0318650143}
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