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Simplifying 4x2 + -47x + 16 = 0 Reorder the terms: 16 + -47x + 4x2 = 0 Solving 16 + -47x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4 + -11.75x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -11.75x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -11.75x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -11.75x + x2 = 0 + -4 -11.75x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -11.75x + x2 = -4 The x term is -11.75x. Take half its coefficient (-5.875). Square it (34.515625) and add it to both sides. Add '34.515625' to each side of the equation. -11.75x + 34.515625 + x2 = -4 + 34.515625 Reorder the terms: 34.515625 + -11.75x + x2 = -4 + 34.515625 Combine like terms: -4 + 34.515625 = 30.515625 34.515625 + -11.75x + x2 = 30.515625 Factor a perfect square on the left side: (x + -5.875)(x + -5.875) = 30.515625 Calculate the square root of the right side: 5.524094948 Break this problem into two subproblems by setting (x + -5.875) equal to 5.524094948 and -5.524094948.Subproblem 1
x + -5.875 = 5.524094948 Simplifying x + -5.875 = 5.524094948 Reorder the terms: -5.875 + x = 5.524094948 Solving -5.875 + x = 5.524094948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.875' to each side of the equation. -5.875 + 5.875 + x = 5.524094948 + 5.875 Combine like terms: -5.875 + 5.875 = 0.000 0.000 + x = 5.524094948 + 5.875 x = 5.524094948 + 5.875 Combine like terms: 5.524094948 + 5.875 = 11.399094948 x = 11.399094948 Simplifying x = 11.399094948Subproblem 2
x + -5.875 = -5.524094948 Simplifying x + -5.875 = -5.524094948 Reorder the terms: -5.875 + x = -5.524094948 Solving -5.875 + x = -5.524094948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.875' to each side of the equation. -5.875 + 5.875 + x = -5.524094948 + 5.875 Combine like terms: -5.875 + 5.875 = 0.000 0.000 + x = -5.524094948 + 5.875 x = -5.524094948 + 5.875 Combine like terms: -5.524094948 + 5.875 = 0.350905052 x = 0.350905052 Simplifying x = 0.350905052Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.399094948, 0.350905052}
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