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Simplifying 6x2 + -10x = 3x + 6 Reorder the terms: -10x + 6x2 = 3x + 6 Reorder the terms: -10x + 6x2 = 6 + 3x Solving -10x + 6x2 = 6 + 3x Solving for variable 'x'. Reorder the terms: -6 + -10x + -3x + 6x2 = 6 + 3x + -6 + -3x Combine like terms: -10x + -3x = -13x -6 + -13x + 6x2 = 6 + 3x + -6 + -3x Reorder the terms: -6 + -13x + 6x2 = 6 + -6 + 3x + -3x Combine like terms: 6 + -6 = 0 -6 + -13x + 6x2 = 0 + 3x + -3x -6 + -13x + 6x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -6 + -13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.166666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.166666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.166666667x + x2 = 0 + 1 -2.166666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.166666667x + x2 = 1 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = 1 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = 1 + 1.173611113 Combine like terms: 1 + 1.173611113 = 2.173611113 1.173611113 + -2.166666667x + x2 = 2.173611113 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 2.173611113 Calculate the square root of the right side: 1.474317168 Break this problem into two subproblems by setting (x + -1.083333334) equal to 1.474317168 and -1.474317168.Subproblem 1
x + -1.083333334 = 1.474317168 Simplifying x + -1.083333334 = 1.474317168 Reorder the terms: -1.083333334 + x = 1.474317168 Solving -1.083333334 + x = 1.474317168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 1.474317168 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 1.474317168 + 1.083333334 x = 1.474317168 + 1.083333334 Combine like terms: 1.474317168 + 1.083333334 = 2.557650502 x = 2.557650502 Simplifying x = 2.557650502Subproblem 2
x + -1.083333334 = -1.474317168 Simplifying x + -1.083333334 = -1.474317168 Reorder the terms: -1.083333334 + x = -1.474317168 Solving -1.083333334 + x = -1.474317168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -1.474317168 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -1.474317168 + 1.083333334 x = -1.474317168 + 1.083333334 Combine like terms: -1.474317168 + 1.083333334 = -0.390983834 x = -0.390983834 Simplifying x = -0.390983834Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.557650502, -0.390983834}
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