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Simplifying 6x2 + 25x + 12 = 0 Reorder the terms: 12 + 25x + 6x2 = 0 Solving 12 + 25x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2 + 4.166666667x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 4.166666667x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 4.166666667x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4.166666667x + x2 = 0 + -2 4.166666667x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 4.166666667x + x2 = -2 The x term is 4.166666667x. Take half its coefficient (2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. 4.166666667x + 4.340277781 + x2 = -2 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667x + x2 = -2 + 4.340277781 Combine like terms: -2 + 4.340277781 = 2.340277781 4.340277781 + 4.166666667x + x2 = 2.340277781 Factor a perfect square on the left side: (x + 2.083333334)(x + 2.083333334) = 2.340277781 Calculate the square root of the right side: 1.529796647 Break this problem into two subproblems by setting (x + 2.083333334) equal to 1.529796647 and -1.529796647.Subproblem 1
x + 2.083333334 = 1.529796647 Simplifying x + 2.083333334 = 1.529796647 Reorder the terms: 2.083333334 + x = 1.529796647 Solving 2.083333334 + x = 1.529796647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = 1.529796647 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = 1.529796647 + -2.083333334 x = 1.529796647 + -2.083333334 Combine like terms: 1.529796647 + -2.083333334 = -0.553536687 x = -0.553536687 Simplifying x = -0.553536687Subproblem 2
x + 2.083333334 = -1.529796647 Simplifying x + 2.083333334 = -1.529796647 Reorder the terms: 2.083333334 + x = -1.529796647 Solving 2.083333334 + x = -1.529796647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = -1.529796647 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = -1.529796647 + -2.083333334 x = -1.529796647 + -2.083333334 Combine like terms: -1.529796647 + -2.083333334 = -3.613129981 x = -3.613129981 Simplifying x = -3.613129981Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.553536687, -3.613129981}
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