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Simplifying 12x2 + -5x + -10 = 0 Reorder the terms: -10 + -5x + 12x2 = 0 Solving -10 + -5x + 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'. -0.8333333333 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -0.4166666667x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -0.4166666667x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -0.4166666667x + x2 = 0 + 0.8333333333 -0.4166666667x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -0.4166666667x + x2 = 0.8333333333 The x term is -0.4166666667x. Take half its coefficient (-0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. -0.4166666667x + 0.04340277781 + x2 = 0.8333333333 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = 0.8333333333 + 0.04340277781 Combine like terms: 0.8333333333 + 0.04340277781 = 0.87673611111 0.04340277781 + -0.4166666667x + x2 = 0.87673611111 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = 0.87673611111 Calculate the square root of the right side: 0.936341877 Break this problem into two subproblems by setting (x + -0.2083333334) equal to 0.936341877 and -0.936341877.Subproblem 1
x + -0.2083333334 = 0.936341877 Simplifying x + -0.2083333334 = 0.936341877 Reorder the terms: -0.2083333334 + x = 0.936341877 Solving -0.2083333334 + x = 0.936341877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + x = 0.936341877 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = 0.936341877 + 0.2083333334 x = 0.936341877 + 0.2083333334 Combine like terms: 0.936341877 + 0.2083333334 = 1.1446752104 x = 1.1446752104 Simplifying x = 1.1446752104Subproblem 2
x + -0.2083333334 = -0.936341877 Simplifying x + -0.2083333334 = -0.936341877 Reorder the terms: -0.2083333334 + x = -0.936341877 Solving -0.2083333334 + x = -0.936341877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + x = -0.936341877 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = -0.936341877 + 0.2083333334 x = -0.936341877 + 0.2083333334 Combine like terms: -0.936341877 + 0.2083333334 = -0.7280085436 x = -0.7280085436 Simplifying x = -0.7280085436Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1446752104, -0.7280085436}
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