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Simplifying -1x4 + 13x2 + -3 = 0 Reorder the terms: -3 + 13x2 + -1x4 = 0 Solving -3 + 13x2 + -1x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -13x2 + x4 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -13x2 + -3 + x4 = 0 + -3 Reorder the terms: 3 + -3 + -13x2 + x4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -13x2 + x4 = 0 + -3 -13x2 + x4 = 0 + -3 Combine like terms: 0 + -3 = -3 -13x2 + x4 = -3 The x term is -13x2. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x2 + 42.25 + x4 = -3 + 42.25 Reorder the terms: 42.25 + -13x2 + x4 = -3 + 42.25 Combine like terms: -3 + 42.25 = 39.25 42.25 + -13x2 + x4 = 39.25 Factor a perfect square on the left side: (x2 + -6.5)(x2 + -6.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x2 + -6.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x2 + -6.5 = 6.264982043 Simplifying x2 + -6.5 = 6.264982043 Reorder the terms: -6.5 + x2 = 6.264982043 Solving -6.5 + x2 = 6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x2 = 6.264982043 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = 6.264982043 + 6.5 x2 = 6.264982043 + 6.5 Combine like terms: 6.264982043 + 6.5 = 12.764982043 x2 = 12.764982043 Simplifying x2 = 12.764982043 Take the square root of each side: x = {-3.572811504, 3.572811504}Subproblem 2
x2 + -6.5 = -6.264982043 Simplifying x2 + -6.5 = -6.264982043 Reorder the terms: -6.5 + x2 = -6.264982043 Solving -6.5 + x2 = -6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x2 = -6.264982043 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = -6.264982043 + 6.5 x2 = -6.264982043 + 6.5 Combine like terms: -6.264982043 + 6.5 = 0.235017957 x2 = 0.235017957 Simplifying x2 = 0.235017957 Take the square root of each side: x = {-0.484786507, 0.484786507}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.572811504, 3.572811504, -0.484786507, 0.484786507}
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