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Simplifying 10x4 + -21x2 + 4 = 0 Reorder the terms: 4 + -21x2 + 10x4 = 0 Solving 4 + -21x2 + 10x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.4 + -2.1x2 + x4 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -2.1x2 + -0.4 + x4 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -2.1x2 + x4 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -2.1x2 + x4 = 0 + -0.4 -2.1x2 + x4 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -2.1x2 + x4 = -0.4 The x term is -2.1x2. Take half its coefficient (-1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. -2.1x2 + 1.1025 + x4 = -0.4 + 1.1025 Reorder the terms: 1.1025 + -2.1x2 + x4 = -0.4 + 1.1025 Combine like terms: -0.4 + 1.1025 = 0.7025 1.1025 + -2.1x2 + x4 = 0.7025 Factor a perfect square on the left side: (x2 + -1.05)(x2 + -1.05) = 0.7025 Calculate the square root of the right side: 0.838152731 Break this problem into two subproblems by setting (x2 + -1.05) equal to 0.838152731 and -0.838152731.Subproblem 1
x2 + -1.05 = 0.838152731 Simplifying x2 + -1.05 = 0.838152731 Reorder the terms: -1.05 + x2 = 0.838152731 Solving -1.05 + x2 = 0.838152731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x2 = 0.838152731 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x2 = 0.838152731 + 1.05 x2 = 0.838152731 + 1.05 Combine like terms: 0.838152731 + 1.05 = 1.888152731 x2 = 1.888152731 Simplifying x2 = 1.888152731 Take the square root of each side: x = {-1.374100699, 1.374100699}Subproblem 2
x2 + -1.05 = -0.838152731 Simplifying x2 + -1.05 = -0.838152731 Reorder the terms: -1.05 + x2 = -0.838152731 Solving -1.05 + x2 = -0.838152731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x2 = -0.838152731 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x2 = -0.838152731 + 1.05 x2 = -0.838152731 + 1.05 Combine like terms: -0.838152731 + 1.05 = 0.211847269 x2 = 0.211847269 Simplifying x2 = 0.211847269 Take the square root of each side: x = {-0.460268692, 0.460268692}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.374100699, 1.374100699, -0.460268692, 0.460268692}
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