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Simplifying -6x2 + -8x + 13 + -7 + -4x + -13x = 0 Reorder the terms: 13 + -7 + -8x + -4x + -13x + -6x2 = 0 Combine like terms: 13 + -7 = 6 6 + -8x + -4x + -13x + -6x2 = 0 Combine like terms: -8x + -4x = -12x 6 + -12x + -13x + -6x2 = 0 Combine like terms: -12x + -13x = -25x 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 = 0.227570771 x = 0.227570771 Simplifying x = 0.227570771Subproblem 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 = -4.394237439 x = -4.394237439 Simplifying x = -4.394237439Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.227570771, -4.394237439}
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