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Simplifying 12x2 = 5x + 9 Reorder the terms: 12x2 = 9 + 5x Solving 12x2 = 9 + 5x Solving for variable 'x'. Reorder the terms: -9 + -5x + 12x2 = 9 + 5x + -9 + -5x Reorder the terms: -9 + -5x + 12x2 = 9 + -9 + 5x + -5x Combine like terms: 9 + -9 = 0 -9 + -5x + 12x2 = 0 + 5x + -5x -9 + -5x + 12x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -9 + -5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.75 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.4166666667x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.4166666667x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.4166666667x + x2 = 0 + 0.75 -0.4166666667x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.4166666667x + x2 = 0.75 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 = 0.75 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = 0.75 + 0.04340277781 Combine like terms: 0.75 + 0.04340277781 = 0.79340277781 0.04340277781 + -0.4166666667x + x2 = 0.79340277781 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = 0.79340277781 Calculate the square root of the right side: 0.890731597 Break this problem into two subproblems by setting (x + -0.2083333334) equal to 0.890731597 and -0.890731597.Subproblem 1
x + -0.2083333334 = 0.890731597 Simplifying x + -0.2083333334 = 0.890731597 Reorder the terms: -0.2083333334 + x = 0.890731597 Solving -0.2083333334 + x = 0.890731597 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 = 0.890731597 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = 0.890731597 + 0.2083333334 x = 0.890731597 + 0.2083333334 Combine like terms: 0.890731597 + 0.2083333334 = 1.0990649304 x = 1.0990649304 Simplifying x = 1.0990649304Subproblem 2
x + -0.2083333334 = -0.890731597 Simplifying x + -0.2083333334 = -0.890731597 Reorder the terms: -0.2083333334 + x = -0.890731597 Solving -0.2083333334 + x = -0.890731597 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 = -0.890731597 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = -0.890731597 + 0.2083333334 x = -0.890731597 + 0.2083333334 Combine like terms: -0.890731597 + 0.2083333334 = -0.6823982636 x = -0.6823982636 Simplifying x = -0.6823982636Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0990649304, -0.6823982636}
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