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Simplifying 2x2 + 44x + 242 = 5x2 Reorder the terms: 242 + 44x + 2x2 = 5x2 Solving 242 + 44x + 2x2 = 5x2 Solving for variable 'x'. Combine like terms: 2x2 + -5x2 = -3x2 242 + 44x + -3x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 242 + 44x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -80.66666667 + -14.66666667x + x2 = 0 Move the constant term to the right: Add '80.66666667' to each side of the equation. -80.66666667 + -14.66666667x + 80.66666667 + x2 = 0 + 80.66666667 Reorder the terms: -80.66666667 + 80.66666667 + -14.66666667x + x2 = 0 + 80.66666667 Combine like terms: -80.66666667 + 80.66666667 = 0.00000000 0.00000000 + -14.66666667x + x2 = 0 + 80.66666667 -14.66666667x + x2 = 0 + 80.66666667 Combine like terms: 0 + 80.66666667 = 80.66666667 -14.66666667x + x2 = 80.66666667 The x term is -14.66666667x. Take half its coefficient (-7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. -14.66666667x + 53.77777780 + x2 = 80.66666667 + 53.77777780 Reorder the terms: 53.77777780 + -14.66666667x + x2 = 80.66666667 + 53.77777780 Combine like terms: 80.66666667 + 53.77777780 = 134.44444447 53.77777780 + -14.66666667x + x2 = 134.44444447 Factor a perfect square on the left side: (x + -7.333333335)(x + -7.333333335) = 134.44444447 Calculate the square root of the right side: 11.595018088 Break this problem into two subproblems by setting (x + -7.333333335) equal to 11.595018088 and -11.595018088.Subproblem 1
x + -7.333333335 = 11.595018088 Simplifying x + -7.333333335 = 11.595018088 Reorder the terms: -7.333333335 + x = 11.595018088 Solving -7.333333335 + x = 11.595018088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + x = 11.595018088 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + x = 11.595018088 + 7.333333335 x = 11.595018088 + 7.333333335 Combine like terms: 11.595018088 + 7.333333335 = 18.928351423 x = 18.928351423 Simplifying x = 18.928351423Subproblem 2
x + -7.333333335 = -11.595018088 Simplifying x + -7.333333335 = -11.595018088 Reorder the terms: -7.333333335 + x = -11.595018088 Solving -7.333333335 + x = -11.595018088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + x = -11.595018088 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + x = -11.595018088 + 7.333333335 x = -11.595018088 + 7.333333335 Combine like terms: -11.595018088 + 7.333333335 = -4.261684753 x = -4.261684753 Simplifying x = -4.261684753Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.928351423, -4.261684753}
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