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Simplifying 12x2 + -20x + -7 = 0 Reorder the terms: -7 + -20x + 12x2 = 0 Solving -7 + -20x + 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'. -0.5833333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + -1.666666667x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + -1.666666667x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + -1.666666667x + x2 = 0 + 0.5833333333 -1.666666667x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 -1.666666667x + x2 = 0.5833333333 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 0.5833333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 0.5833333333 + 0.6944444447 Combine like terms: 0.5833333333 + 0.6944444447 = 1.277777778 0.6944444447 + -1.666666667x + x2 = 1.277777778 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 1.277777778 Calculate the square root of the right side: 1.130388331 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.130388331 and -1.130388331.Subproblem 1
x + -0.8333333335 = 1.130388331 Simplifying x + -0.8333333335 = 1.130388331 Reorder the terms: -0.8333333335 + x = 1.130388331 Solving -0.8333333335 + x = 1.130388331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.130388331 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.130388331 + 0.8333333335 x = 1.130388331 + 0.8333333335 Combine like terms: 1.130388331 + 0.8333333335 = 1.9637216645 x = 1.9637216645 Simplifying x = 1.9637216645Subproblem 2
x + -0.8333333335 = -1.130388331 Simplifying x + -0.8333333335 = -1.130388331 Reorder the terms: -0.8333333335 + x = -1.130388331 Solving -0.8333333335 + x = -1.130388331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.130388331 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.130388331 + 0.8333333335 x = -1.130388331 + 0.8333333335 Combine like terms: -1.130388331 + 0.8333333335 = -0.2970549975 x = -0.2970549975 Simplifying x = -0.2970549975Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9637216645, -0.2970549975}
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