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Simplifying 6x2 + -20 = 29x Reorder the terms: -20 + 6x2 = 29x Solving -20 + 6x2 = 29x Solving for variable 'x'. Reorder the terms: -20 + -29x + 6x2 = 29x + -29x Combine like terms: 29x + -29x = 0 -20 + -29x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.333333333 + -4.833333333x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -4.833333333x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -4.833333333x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -4.833333333x + x2 = 0 + 3.333333333 -4.833333333x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -4.833333333x + x2 = 3.333333333 The x term is -4.833333333x. Take half its coefficient (-2.416666667). Square it (5.840277779) and add it to both sides. Add '5.840277779' to each side of the equation. -4.833333333x + 5.840277779 + x2 = 3.333333333 + 5.840277779 Reorder the terms: 5.840277779 + -4.833333333x + x2 = 3.333333333 + 5.840277779 Combine like terms: 3.333333333 + 5.840277779 = 9.173611112 5.840277779 + -4.833333333x + x2 = 9.173611112 Factor a perfect square on the left side: (x + -2.416666667)(x + -2.416666667) = 9.173611112 Calculate the square root of the right side: 3.028796974 Break this problem into two subproblems by setting (x + -2.416666667) equal to 3.028796974 and -3.028796974.Subproblem 1
x + -2.416666667 = 3.028796974 Simplifying x + -2.416666667 = 3.028796974 Reorder the terms: -2.416666667 + x = 3.028796974 Solving -2.416666667 + x = 3.028796974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.416666667' to each side of the equation. -2.416666667 + 2.416666667 + x = 3.028796974 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + x = 3.028796974 + 2.416666667 x = 3.028796974 + 2.416666667 Combine like terms: 3.028796974 + 2.416666667 = 5.445463641 x = 5.445463641 Simplifying x = 5.445463641Subproblem 2
x + -2.416666667 = -3.028796974 Simplifying x + -2.416666667 = -3.028796974 Reorder the terms: -2.416666667 + x = -3.028796974 Solving -2.416666667 + x = -3.028796974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.416666667' to each side of the equation. -2.416666667 + 2.416666667 + x = -3.028796974 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + x = -3.028796974 + 2.416666667 x = -3.028796974 + 2.416666667 Combine like terms: -3.028796974 + 2.416666667 = -0.612130307 x = -0.612130307 Simplifying x = -0.612130307Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.445463641, -0.612130307}
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