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Simplifying 12x2 + 5x + -19 = 0 Reorder the terms: -19 + 5x + 12x2 = 0 Solving -19 + 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'. -1.583333333 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '1.583333333' to each side of the equation. -1.583333333 + 0.4166666667x + 1.583333333 + x2 = 0 + 1.583333333 Reorder the terms: -1.583333333 + 1.583333333 + 0.4166666667x + x2 = 0 + 1.583333333 Combine like terms: -1.583333333 + 1.583333333 = 0.000000000 0.000000000 + 0.4166666667x + x2 = 0 + 1.583333333 0.4166666667x + x2 = 0 + 1.583333333 Combine like terms: 0 + 1.583333333 = 1.583333333 0.4166666667x + x2 = 1.583333333 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 = 1.583333333 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 1.583333333 + 0.04340277781 Combine like terms: 1.583333333 + 0.04340277781 = 1.62673611081 0.04340277781 + 0.4166666667x + x2 = 1.62673611081 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 1.62673611081 Calculate the square root of the right side: 1.275435655 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 1.275435655 and -1.275435655.Subproblem 1
x + 0.2083333334 = 1.275435655 Simplifying x + 0.2083333334 = 1.275435655 Reorder the terms: 0.2083333334 + x = 1.275435655 Solving 0.2083333334 + x = 1.275435655 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 = 1.275435655 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 1.275435655 + -0.2083333334 x = 1.275435655 + -0.2083333334 Combine like terms: 1.275435655 + -0.2083333334 = 1.0671023216 x = 1.0671023216 Simplifying x = 1.0671023216Subproblem 2
x + 0.2083333334 = -1.275435655 Simplifying x + 0.2083333334 = -1.275435655 Reorder the terms: 0.2083333334 + x = -1.275435655 Solving 0.2083333334 + x = -1.275435655 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 = -1.275435655 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -1.275435655 + -0.2083333334 x = -1.275435655 + -0.2083333334 Combine like terms: -1.275435655 + -0.2083333334 = -1.4837689884 x = -1.4837689884 Simplifying x = -1.4837689884Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0671023216, -1.4837689884}
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