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Simplifying 6x2 + 25x + 9 = 0 Reorder the terms: 9 + 25x + 6x2 = 0 Solving 9 + 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'. 1.5 + 4.166666667x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 4.166666667x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 4.166666667x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 4.166666667x + x2 = 0 + -1.5 4.166666667x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 4.166666667x + x2 = -1.5 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 = -1.5 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667x + x2 = -1.5 + 4.340277781 Combine like terms: -1.5 + 4.340277781 = 2.840277781 4.340277781 + 4.166666667x + x2 = 2.840277781 Factor a perfect square on the left side: (x + 2.083333334)(x + 2.083333334) = 2.840277781 Calculate the square root of the right side: 1.685312369 Break this problem into two subproblems by setting (x + 2.083333334) equal to 1.685312369 and -1.685312369.Subproblem 1
x + 2.083333334 = 1.685312369 Simplifying x + 2.083333334 = 1.685312369 Reorder the terms: 2.083333334 + x = 1.685312369 Solving 2.083333334 + x = 1.685312369 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 = 1.685312369 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = 1.685312369 + -2.083333334 x = 1.685312369 + -2.083333334 Combine like terms: 1.685312369 + -2.083333334 = -0.398020965 x = -0.398020965 Simplifying x = -0.398020965Subproblem 2
x + 2.083333334 = -1.685312369 Simplifying x + 2.083333334 = -1.685312369 Reorder the terms: 2.083333334 + x = -1.685312369 Solving 2.083333334 + x = -1.685312369 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 = -1.685312369 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = -1.685312369 + -2.083333334 x = -1.685312369 + -2.083333334 Combine like terms: -1.685312369 + -2.083333334 = -3.768645703 x = -3.768645703 Simplifying x = -3.768645703Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.398020965, -3.768645703}
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