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Simplifying 4x4 + -21x2 + 10 = 0 Reorder the terms: 10 + -21x2 + 4x4 = 0 Solving 10 + -21x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.5 + -5.25x2 + x4 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -5.25x2 + -2.5 + x4 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -5.25x2 + x4 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -5.25x2 + x4 = 0 + -2.5 -5.25x2 + x4 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -5.25x2 + x4 = -2.5 The x term is -5.25x2. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x2 + 6.890625 + x4 = -2.5 + 6.890625 Reorder the terms: 6.890625 + -5.25x2 + x4 = -2.5 + 6.890625 Combine like terms: -2.5 + 6.890625 = 4.390625 6.890625 + -5.25x2 + x4 = 4.390625 Factor a perfect square on the left side: (x2 + -2.625)(x2 + -2.625) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x2 + -2.625) equal to 2.095381827 and -2.095381827.Subproblem 1
x2 + -2.625 = 2.095381827 Simplifying x2 + -2.625 = 2.095381827 Reorder the terms: -2.625 + x2 = 2.095381827 Solving -2.625 + x2 = 2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x2 = 2.095381827 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x2 = 2.095381827 + 2.625 x2 = 2.095381827 + 2.625 Combine like terms: 2.095381827 + 2.625 = 4.720381827 x2 = 4.720381827 Simplifying x2 = 4.720381827 Take the square root of each side: x = {-2.172643972, 2.172643972}Subproblem 2
x2 + -2.625 = -2.095381827 Simplifying x2 + -2.625 = -2.095381827 Reorder the terms: -2.625 + x2 = -2.095381827 Solving -2.625 + x2 = -2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x2 = -2.095381827 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x2 = -2.095381827 + 2.625 x2 = -2.095381827 + 2.625 Combine like terms: -2.095381827 + 2.625 = 0.529618173 x2 = 0.529618173 Simplifying x2 = 0.529618173 Take the square root of each side: x = {-0.727748702, 0.727748702}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.172643972, 2.172643972, -0.727748702, 0.727748702}
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