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Simplifying 3x2 + -35x + 42 = 0 Reorder the terms: 42 + -35x + 3x2 = 0 Solving 42 + -35x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 14 + -11.66666667x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -11.66666667x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -11.66666667x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -11.66666667x + x2 = 0 + -14 -11.66666667x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -11.66666667x + x2 = -14 The x term is -11.66666667x. Take half its coefficient (-5.833333335). Square it (34.02777780) and add it to both sides. Add '34.02777780' to each side of the equation. -11.66666667x + 34.02777780 + x2 = -14 + 34.02777780 Reorder the terms: 34.02777780 + -11.66666667x + x2 = -14 + 34.02777780 Combine like terms: -14 + 34.02777780 = 20.0277778 34.02777780 + -11.66666667x + x2 = 20.0277778 Factor a perfect square on the left side: (x + -5.833333335)(x + -5.833333335) = 20.0277778 Calculate the square root of the right side: 4.47524053 Break this problem into two subproblems by setting (x + -5.833333335) equal to 4.47524053 and -4.47524053.Subproblem 1
x + -5.833333335 = 4.47524053 Simplifying x + -5.833333335 = 4.47524053 Reorder the terms: -5.833333335 + x = 4.47524053 Solving -5.833333335 + x = 4.47524053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + x = 4.47524053 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = 4.47524053 + 5.833333335 x = 4.47524053 + 5.833333335 Combine like terms: 4.47524053 + 5.833333335 = 10.308573865 x = 10.308573865 Simplifying x = 10.308573865Subproblem 2
x + -5.833333335 = -4.47524053 Simplifying x + -5.833333335 = -4.47524053 Reorder the terms: -5.833333335 + x = -4.47524053 Solving -5.833333335 + x = -4.47524053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + x = -4.47524053 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = -4.47524053 + 5.833333335 x = -4.47524053 + 5.833333335 Combine like terms: -4.47524053 + 5.833333335 = 1.358092805 x = 1.358092805 Simplifying x = 1.358092805Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.308573865, 1.358092805}
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