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Simplifying 3x4 + -21x2 + 17 = 0 Reorder the terms: 17 + -21x2 + 3x4 = 0 Solving 17 + -21x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.666666667 + -7x2 + x4 = 0 Move the constant term to the right: Add '-5.666666667' to each side of the equation. 5.666666667 + -7x2 + -5.666666667 + x4 = 0 + -5.666666667 Reorder the terms: 5.666666667 + -5.666666667 + -7x2 + x4 = 0 + -5.666666667 Combine like terms: 5.666666667 + -5.666666667 = 0.000000000 0.000000000 + -7x2 + x4 = 0 + -5.666666667 -7x2 + x4 = 0 + -5.666666667 Combine like terms: 0 + -5.666666667 = -5.666666667 -7x2 + x4 = -5.666666667 The x term is -7x2. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x2 + 12.25 + x4 = -5.666666667 + 12.25 Reorder the terms: 12.25 + -7x2 + x4 = -5.666666667 + 12.25 Combine like terms: -5.666666667 + 12.25 = 6.583333333 12.25 + -7x2 + x4 = 6.583333333 Factor a perfect square on the left side: (x2 + -3.5)(x2 + -3.5) = 6.583333333 Calculate the square root of the right side: 2.56580072 Break this problem into two subproblems by setting (x2 + -3.5) equal to 2.56580072 and -2.56580072.Subproblem 1
x2 + -3.5 = 2.56580072 Simplifying x2 + -3.5 = 2.56580072 Reorder the terms: -3.5 + x2 = 2.56580072 Solving -3.5 + x2 = 2.56580072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = 2.56580072 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = 2.56580072 + 3.5 x2 = 2.56580072 + 3.5 Combine like terms: 2.56580072 + 3.5 = 6.06580072 x2 = 6.06580072 Simplifying x2 = 6.06580072 Take the square root of each side: x = {-2.462884634, 2.462884634}Subproblem 2
x2 + -3.5 = -2.56580072 Simplifying x2 + -3.5 = -2.56580072 Reorder the terms: -3.5 + x2 = -2.56580072 Solving -3.5 + x2 = -2.56580072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = -2.56580072 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = -2.56580072 + 3.5 x2 = -2.56580072 + 3.5 Combine like terms: -2.56580072 + 3.5 = 0.93419928 x2 = 0.93419928 Simplifying x2 = 0.93419928 Take the square root of each side: x = {-0.966539849, 0.966539849}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.462884634, 2.462884634, -0.966539849, 0.966539849}
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