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Simplifying 2x5 + 2x + -144x3 = 0 Reorder the terms: 2x + -144x3 + 2x5 = 0 Solving 2x + -144x3 + 2x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(1 + -72x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + -72x2 + x4)' equal to zero and attempt to solve: Simplifying 1 + -72x2 + x4 = 0 Solving 1 + -72x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -72x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + -72x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -72x2 + x4 = 0 + -1 -72x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 -72x2 + x4 = -1 The x term is -72x2. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x2 + 1296 + x4 = -1 + 1296 Reorder the terms: 1296 + -72x2 + x4 = -1 + 1296 Combine like terms: -1 + 1296 = 1295 1296 + -72x2 + x4 = 1295 Factor a perfect square on the left side: (x2 + -36)(x2 + -36) = 1295 Calculate the square root of the right side: 35.986108431 Break this problem into two subproblems by setting (x2 + -36) equal to 35.986108431 and -35.986108431.Subproblem 1
x2 + -36 = 35.986108431 Simplifying x2 + -36 = 35.986108431 Reorder the terms: -36 + x2 = 35.986108431 Solving -36 + x2 = 35.986108431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x2 = 35.986108431 + 36 Combine like terms: -36 + 36 = 0 0 + x2 = 35.986108431 + 36 x2 = 35.986108431 + 36 Combine like terms: 35.986108431 + 36 = 71.986108431 x2 = 71.986108431 Simplifying x2 = 71.986108431 Take the square root of each side: x = {-8.484462766, 8.484462766}Subproblem 2
x2 + -36 = -35.986108431 Simplifying x2 + -36 = -35.986108431 Reorder the terms: -36 + x2 = -35.986108431 Solving -36 + x2 = -35.986108431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x2 = -35.986108431 + 36 Combine like terms: -36 + 36 = 0 0 + x2 = -35.986108431 + 36 x2 = -35.986108431 + 36 Combine like terms: -35.986108431 + 36 = 0.013891569 x2 = 0.013891569 Simplifying x2 = 0.013891569 Take the square root of each side: x = {-0.1178625, 0.1178625}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.484462766, 8.484462766, -0.1178625, 0.1178625}Solution
x = {0, -8.484462766, 8.484462766, -0.1178625, 0.1178625}
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