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Simplifying 4x4 + -65x2 = -64 Reorder the terms: -65x2 + 4x4 = -64 Solving -65x2 + 4x4 = -64 Solving for variable 'x'. Reorder the terms: 64 + -65x2 + 4x4 = -64 + 64 Combine like terms: -64 + 64 = 0 64 + -65x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 16 + -16.25x2 + x4 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -16.25x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + -16.25x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -16.25x2 + x4 = 0 + -16 -16.25x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 -16.25x2 + x4 = -16 The x term is -16.25x2. Take half its coefficient (-8.125). Square it (66.015625) and add it to both sides. Add '66.015625' to each side of the equation. -16.25x2 + 66.015625 + x4 = -16 + 66.015625 Reorder the terms: 66.015625 + -16.25x2 + x4 = -16 + 66.015625 Combine like terms: -16 + 66.015625 = 50.015625 66.015625 + -16.25x2 + x4 = 50.015625 Factor a perfect square on the left side: (x2 + -8.125)(x2 + -8.125) = 50.015625 Calculate the square root of the right side: 7.07217258 Break this problem into two subproblems by setting (x2 + -8.125) equal to 7.07217258 and -7.07217258.Subproblem 1
x2 + -8.125 = 7.07217258 Simplifying x2 + -8.125 = 7.07217258 Reorder the terms: -8.125 + x2 = 7.07217258 Solving -8.125 + x2 = 7.07217258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.125' to each side of the equation. -8.125 + 8.125 + x2 = 7.07217258 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + x2 = 7.07217258 + 8.125 x2 = 7.07217258 + 8.125 Combine like terms: 7.07217258 + 8.125 = 15.19717258 x2 = 15.19717258 Simplifying x2 = 15.19717258 Take the square root of each side: x = {-3.898355112, 3.898355112}Subproblem 2
x2 + -8.125 = -7.07217258 Simplifying x2 + -8.125 = -7.07217258 Reorder the terms: -8.125 + x2 = -7.07217258 Solving -8.125 + x2 = -7.07217258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.125' to each side of the equation. -8.125 + 8.125 + x2 = -7.07217258 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + x2 = -7.07217258 + 8.125 x2 = -7.07217258 + 8.125 Combine like terms: -7.07217258 + 8.125 = 1.05282742 x2 = 1.05282742 Simplifying x2 = 1.05282742 Take the square root of each side: x = {-1.026073789, 1.026073789}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.898355112, 3.898355112, -1.026073789, 1.026073789}
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