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Simplifying -6x2 + 25x + 6 = 0 Reorder the terms: 6 + 25x + -6x2 = 0 Solving 6 + 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 + -4.166666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4.166666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -4.166666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4.166666667x + x2 = 0 + 1 -4.166666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4.166666667x + x2 = 1 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 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667x + x2 = 1 + 4.340277781 Combine like terms: 1 + 4.340277781 = 5.340277781 4.340277781 + -4.166666667x + x2 = 5.340277781 Factor a perfect square on the left side: (x + -2.083333334)(x + -2.083333334) = 5.340277781 Calculate the square root of the right side: 2.310904105 Break this problem into two subproblems by setting (x + -2.083333334) equal to 2.310904105 and -2.310904105.Subproblem 1
x + -2.083333334 = 2.310904105 Simplifying x + -2.083333334 = 2.310904105 Reorder the terms: -2.083333334 + x = 2.310904105 Solving -2.083333334 + x = 2.310904105 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 = 2.310904105 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = 2.310904105 + 2.083333334 x = 2.310904105 + 2.083333334 Combine like terms: 2.310904105 + 2.083333334 = 4.394237439 x = 4.394237439 Simplifying x = 4.394237439Subproblem 2
x + -2.083333334 = -2.310904105 Simplifying x + -2.083333334 = -2.310904105 Reorder the terms: -2.083333334 + x = -2.310904105 Solving -2.083333334 + x = -2.310904105 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 = -2.310904105 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = -2.310904105 + 2.083333334 x = -2.310904105 + 2.083333334 Combine like terms: -2.310904105 + 2.083333334 = -0.227570771 x = -0.227570771 Simplifying x = -0.227570771Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.394237439, -0.227570771}
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