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Simplifying 13x4 + -17x2 + -20 = 0 Reorder the terms: -20 + -17x2 + 13x4 = 0 Solving -20 + -17x2 + 13x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1.538461538 + -1.307692308x2 + x4 = 0 Move the constant term to the right: Add '1.538461538' to each side of the equation. -1.538461538 + -1.307692308x2 + 1.538461538 + x4 = 0 + 1.538461538 Reorder the terms: -1.538461538 + 1.538461538 + -1.307692308x2 + x4 = 0 + 1.538461538 Combine like terms: -1.538461538 + 1.538461538 = 0.000000000 0.000000000 + -1.307692308x2 + x4 = 0 + 1.538461538 -1.307692308x2 + x4 = 0 + 1.538461538 Combine like terms: 0 + 1.538461538 = 1.538461538 -1.307692308x2 + x4 = 1.538461538 The x term is -1.307692308x2. Take half its coefficient (-0.653846154). Square it (0.4275147931) and add it to both sides. Add '0.4275147931' to each side of the equation. -1.307692308x2 + 0.4275147931 + x4 = 1.538461538 + 0.4275147931 Reorder the terms: 0.4275147931 + -1.307692308x2 + x4 = 1.538461538 + 0.4275147931 Combine like terms: 1.538461538 + 0.4275147931 = 1.9659763311 0.4275147931 + -1.307692308x2 + x4 = 1.9659763311 Factor a perfect square on the left side: (x2 + -0.653846154)(x2 + -0.653846154) = 1.9659763311 Calculate the square root of the right side: 1.402132779 Break this problem into two subproblems by setting (x2 + -0.653846154) equal to 1.402132779 and -1.402132779.Subproblem 1
x2 + -0.653846154 = 1.402132779 Simplifying x2 + -0.653846154 = 1.402132779 Reorder the terms: -0.653846154 + x2 = 1.402132779 Solving -0.653846154 + x2 = 1.402132779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.653846154' to each side of the equation. -0.653846154 + 0.653846154 + x2 = 1.402132779 + 0.653846154 Combine like terms: -0.653846154 + 0.653846154 = 0.000000000 0.000000000 + x2 = 1.402132779 + 0.653846154 x2 = 1.402132779 + 0.653846154 Combine like terms: 1.402132779 + 0.653846154 = 2.055978933 x2 = 2.055978933 Simplifying x2 = 2.055978933 Take the square root of each side: x = {-1.43386852, 1.43386852}Subproblem 2
x2 + -0.653846154 = -1.402132779 Simplifying x2 + -0.653846154 = -1.402132779 Reorder the terms: -0.653846154 + x2 = -1.402132779 Solving -0.653846154 + x2 = -1.402132779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.653846154' to each side of the equation. -0.653846154 + 0.653846154 + x2 = -1.402132779 + 0.653846154 Combine like terms: -0.653846154 + 0.653846154 = 0.000000000 0.000000000 + x2 = -1.402132779 + 0.653846154 x2 = -1.402132779 + 0.653846154 Combine like terms: -1.402132779 + 0.653846154 = -0.748286625 x2 = -0.748286625 Simplifying x2 = -0.748286625 Reorder the terms: 0.748286625 + x2 = -0.748286625 + 0.748286625 Combine like terms: -0.748286625 + 0.748286625 = 0.000000000 0.748286625 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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