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Simplifying 6x2 + -29x + 15 = -9x + 6 Reorder the terms: 15 + -29x + 6x2 = -9x + 6 Reorder the terms: 15 + -29x + 6x2 = 6 + -9x Solving 15 + -29x + 6x2 = 6 + -9x Solving for variable 'x'. Reorder the terms: 15 + -6 + -29x + 9x + 6x2 = 6 + -9x + -6 + 9x Combine like terms: 15 + -6 = 9 9 + -29x + 9x + 6x2 = 6 + -9x + -6 + 9x Combine like terms: -29x + 9x = -20x 9 + -20x + 6x2 = 6 + -9x + -6 + 9x Reorder the terms: 9 + -20x + 6x2 = 6 + -6 + -9x + 9x Combine like terms: 6 + -6 = 0 9 + -20x + 6x2 = 0 + -9x + 9x 9 + -20x + 6x2 = -9x + 9x Combine like terms: -9x + 9x = 0 9 + -20x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -3.333333333x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -3.333333333x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -3.333333333x + x2 = 0 + -1.5 -3.333333333x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -3.333333333x + x2 = -1.5 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -1.5 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -1.5 + 2.777777779 Combine like terms: -1.5 + 2.777777779 = 1.277777779 2.777777779 + -3.333333333x + x2 = 1.277777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 1.277777779 Calculate the square root of the right side: 1.130388331 Break this problem into two subproblems by setting (x + -1.666666667) equal to 1.130388331 and -1.130388331.Subproblem 1
x + -1.666666667 = 1.130388331 Simplifying x + -1.666666667 = 1.130388331 Reorder the terms: -1.666666667 + x = 1.130388331 Solving -1.666666667 + x = 1.130388331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 1.130388331 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 1.130388331 + 1.666666667 x = 1.130388331 + 1.666666667 Combine like terms: 1.130388331 + 1.666666667 = 2.797054998 x = 2.797054998 Simplifying x = 2.797054998Subproblem 2
x + -1.666666667 = -1.130388331 Simplifying x + -1.666666667 = -1.130388331 Reorder the terms: -1.666666667 + x = -1.130388331 Solving -1.666666667 + x = -1.130388331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -1.130388331 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -1.130388331 + 1.666666667 x = -1.130388331 + 1.666666667 Combine like terms: -1.130388331 + 1.666666667 = 0.536278336 x = 0.536278336 Simplifying x = 0.536278336Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.797054998, 0.536278336}
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