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Simplifying 64x4 + -63x2 + 15 = 0 Reorder the terms: 15 + -63x2 + 64x4 = 0 Solving 15 + -63x2 + 64x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. 0.234375 + -0.984375x2 + x4 = 0 Move the constant term to the right: Add '-0.234375' to each side of the equation. 0.234375 + -0.984375x2 + -0.234375 + x4 = 0 + -0.234375 Reorder the terms: 0.234375 + -0.234375 + -0.984375x2 + x4 = 0 + -0.234375 Combine like terms: 0.234375 + -0.234375 = 0.000000 0.000000 + -0.984375x2 + x4 = 0 + -0.234375 -0.984375x2 + x4 = 0 + -0.234375 Combine like terms: 0 + -0.234375 = -0.234375 -0.984375x2 + x4 = -0.234375 The x term is -0.984375x2. Take half its coefficient (-0.4921875). Square it (0.2422485352) and add it to both sides. Add '0.2422485352' to each side of the equation. -0.984375x2 + 0.2422485352 + x4 = -0.234375 + 0.2422485352 Reorder the terms: 0.2422485352 + -0.984375x2 + x4 = -0.234375 + 0.2422485352 Combine like terms: -0.234375 + 0.2422485352 = 0.0078735352 0.2422485352 + -0.984375x2 + x4 = 0.0078735352 Factor a perfect square on the left side: (x2 + -0.4921875)(x2 + -0.4921875) = 0.0078735352 Calculate the square root of the right side: 0.088732943 Break this problem into two subproblems by setting (x2 + -0.4921875) equal to 0.088732943 and -0.088732943.Subproblem 1
x2 + -0.4921875 = 0.088732943 Simplifying x2 + -0.4921875 = 0.088732943 Reorder the terms: -0.4921875 + x2 = 0.088732943 Solving -0.4921875 + x2 = 0.088732943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4921875' to each side of the equation. -0.4921875 + 0.4921875 + x2 = 0.088732943 + 0.4921875 Combine like terms: -0.4921875 + 0.4921875 = 0.0000000 0.0000000 + x2 = 0.088732943 + 0.4921875 x2 = 0.088732943 + 0.4921875 Combine like terms: 0.088732943 + 0.4921875 = 0.580920443 x2 = 0.580920443 Simplifying x2 = 0.580920443 Take the square root of each side: x = {-0.762181371, 0.762181371}Subproblem 2
x2 + -0.4921875 = -0.088732943 Simplifying x2 + -0.4921875 = -0.088732943 Reorder the terms: -0.4921875 + x2 = -0.088732943 Solving -0.4921875 + x2 = -0.088732943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4921875' to each side of the equation. -0.4921875 + 0.4921875 + x2 = -0.088732943 + 0.4921875 Combine like terms: -0.4921875 + 0.4921875 = 0.0000000 0.0000000 + x2 = -0.088732943 + 0.4921875 x2 = -0.088732943 + 0.4921875 Combine like terms: -0.088732943 + 0.4921875 = 0.403454557 x2 = 0.403454557 Simplifying x2 = 0.403454557 Take the square root of each side: x = {-0.635180728, 0.635180728}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.762181371, 0.762181371, -0.635180728, 0.635180728}
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