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Simplifying 35x + 4 = 3x2 Reorder the terms: 4 + 35x = 3x2 Solving 4 + 35x = 3x2 Solving for variable 'x'. Combine like terms: 3x2 + -3x2 = 0 4 + 35x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.333333333 + -11.66666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -11.66666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -11.66666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -11.66666667x + x2 = 0 + 1.333333333 -11.66666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -11.66666667x + x2 = 1.333333333 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 = 1.333333333 + 34.02777780 Reorder the terms: 34.02777780 + -11.66666667x + x2 = 1.333333333 + 34.02777780 Combine like terms: 1.333333333 + 34.02777780 = 35.361111133 34.02777780 + -11.66666667x + x2 = 35.361111133 Factor a perfect square on the left side: (x + -5.833333335)(x + -5.833333335) = 35.361111133 Calculate the square root of the right side: 5.946520927 Break this problem into two subproblems by setting (x + -5.833333335) equal to 5.946520927 and -5.946520927.Subproblem 1
x + -5.833333335 = 5.946520927 Simplifying x + -5.833333335 = 5.946520927 Reorder the terms: -5.833333335 + x = 5.946520927 Solving -5.833333335 + x = 5.946520927 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 = 5.946520927 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = 5.946520927 + 5.833333335 x = 5.946520927 + 5.833333335 Combine like terms: 5.946520927 + 5.833333335 = 11.779854262 x = 11.779854262 Simplifying x = 11.779854262Subproblem 2
x + -5.833333335 = -5.946520927 Simplifying x + -5.833333335 = -5.946520927 Reorder the terms: -5.833333335 + x = -5.946520927 Solving -5.833333335 + x = -5.946520927 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 = -5.946520927 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = -5.946520927 + 5.833333335 x = -5.946520927 + 5.833333335 Combine like terms: -5.946520927 + 5.833333335 = -0.113187592 x = -0.113187592 Simplifying x = -0.113187592Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.779854262, -0.113187592}
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