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Simplifying 12x2 + -5x = 5 Reorder the terms: -5x + 12x2 = 5 Solving -5x + 12x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -5x + 12x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -0.4166666667x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -0.4166666667x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -0.4166666667x + x2 = 0 + 0.4166666667 -0.4166666667x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -0.4166666667x + x2 = 0.4166666667 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 = 0.4166666667 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = 0.4166666667 + 0.04340277781 Combine like terms: 0.4166666667 + 0.04340277781 = 0.46006944451 0.04340277781 + -0.4166666667x + x2 = 0.46006944451 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = 0.46006944451 Calculate the square root of the right side: 0.678284192 Break this problem into two subproblems by setting (x + -0.2083333334) equal to 0.678284192 and -0.678284192.Subproblem 1
x + -0.2083333334 = 0.678284192 Simplifying x + -0.2083333334 = 0.678284192 Reorder the terms: -0.2083333334 + x = 0.678284192 Solving -0.2083333334 + x = 0.678284192 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 = 0.678284192 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = 0.678284192 + 0.2083333334 x = 0.678284192 + 0.2083333334 Combine like terms: 0.678284192 + 0.2083333334 = 0.8866175254 x = 0.8866175254 Simplifying x = 0.8866175254Subproblem 2
x + -0.2083333334 = -0.678284192 Simplifying x + -0.2083333334 = -0.678284192 Reorder the terms: -0.2083333334 + x = -0.678284192 Solving -0.2083333334 + x = -0.678284192 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 = -0.678284192 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = -0.678284192 + 0.2083333334 x = -0.678284192 + 0.2083333334 Combine like terms: -0.678284192 + 0.2083333334 = -0.4699508586 x = -0.4699508586 Simplifying x = -0.4699508586Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8866175254, -0.4699508586}
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