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Simplifying 5x4 + -47x2 + 56 = 0 Reorder the terms: 56 + -47x2 + 5x4 = 0 Solving 56 + -47x2 + 5x4 = 0 Solving for variable 'x'. Factor a trinomial. (7 + -5x2)(8 + -1x2) = 0Subproblem 1
Set the factor '(7 + -5x2)' equal to zero and attempt to solve: Simplifying 7 + -5x2 = 0 Solving 7 + -5x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x2 = 0 + -7 -5x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -5x2 = -7 Divide each side by '-5'. x2 = 1.4 Simplifying x2 = 1.4 Take the square root of each side: x = {-1.183215957, 1.183215957}Subproblem 2
Set the factor '(8 + -1x2)' equal to zero and attempt to solve: Simplifying 8 + -1x2 = 0 Solving 8 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x2 = 0 + -8 -1x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -1x2 = -8 Divide each side by '-1'. x2 = 8 Simplifying x2 = 8 Take the square root of each side: x = {-2.828427125, 2.828427125}Solution
x = {-1.183215957, 1.183215957, -2.828427125, 2.828427125}
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