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Simplifying 5.1x2 + -1.7x + -3.2 = 0 Reorder the terms: -3.2 + -1.7x + 5.1x2 = 0 Solving -3.2 + -1.7x + 5.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.1 the coefficient of the squared term: Divide each side by '5.1'. -0.6274509804 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.6274509804' to each side of the equation. -0.6274509804 + -0.3333333333x + 0.6274509804 + x2 = 0 + 0.6274509804 Reorder the terms: -0.6274509804 + 0.6274509804 + -0.3333333333x + x2 = 0 + 0.6274509804 Combine like terms: -0.6274509804 + 0.6274509804 = 0.0000000000 0.0000000000 + -0.3333333333x + x2 = 0 + 0.6274509804 -0.3333333333x + x2 = 0 + 0.6274509804 Combine like terms: 0 + 0.6274509804 = 0.6274509804 -0.3333333333x + x2 = 0.6274509804 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 0.6274509804 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.6274509804 + 0.02777777779 Combine like terms: 0.6274509804 + 0.02777777779 = 0.65522875819 0.02777777779 + -0.3333333333x + x2 = 0.65522875819 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.65522875819 Calculate the square root of the right side: 0.809462018 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.809462018 and -0.809462018.Subproblem 1
x + -0.1666666667 = 0.809462018 Simplifying x + -0.1666666667 = 0.809462018 Reorder the terms: -0.1666666667 + x = 0.809462018 Solving -0.1666666667 + x = 0.809462018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.809462018 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.809462018 + 0.1666666667 x = 0.809462018 + 0.1666666667 Combine like terms: 0.809462018 + 0.1666666667 = 0.9761286847 x = 0.9761286847 Simplifying x = 0.9761286847Subproblem 2
x + -0.1666666667 = -0.809462018 Simplifying x + -0.1666666667 = -0.809462018 Reorder the terms: -0.1666666667 + x = -0.809462018 Solving -0.1666666667 + x = -0.809462018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.809462018 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.809462018 + 0.1666666667 x = -0.809462018 + 0.1666666667 Combine like terms: -0.809462018 + 0.1666666667 = -0.6427953513 x = -0.6427953513 Simplifying x = -0.6427953513Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9761286847, -0.6427953513}
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