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Simplifying 4x4 = 5(4x2 + -5) Reorder the terms: 4x4 = 5(-5 + 4x2) 4x4 = (-5 * 5 + 4x2 * 5) 4x4 = (-25 + 20x2) Solving 4x4 = -25 + 20x2 Solving for variable 'x'. Reorder the terms: 25 + -20x2 + 4x4 = -25 + 20x2 + 25 + -20x2 Reorder the terms: 25 + -20x2 + 4x4 = -25 + 25 + 20x2 + -20x2 Combine like terms: -25 + 25 = 0 25 + -20x2 + 4x4 = 0 + 20x2 + -20x2 25 + -20x2 + 4x4 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 25 + -20x2 + 4x4 = 0 Factor a trinomial. (5 + -2x2)(5 + -2x2) = 0Subproblem 1
Set the factor '(5 + -2x2)' equal to zero and attempt to solve: Simplifying 5 + -2x2 = 0 Solving 5 + -2x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x2 = 0 + -5 -2x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2x2 = -5 Divide each side by '-2'. x2 = 2.5 Simplifying x2 = 2.5 Take the square root of each side: x = {-1.58113883, 1.58113883}Subproblem 2
Set the factor '(5 + -2x2)' equal to zero and attempt to solve: Simplifying 5 + -2x2 = 0 Solving 5 + -2x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x2 = 0 + -5 -2x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2x2 = -5 Divide each side by '-2'. x2 = 2.5 Simplifying x2 = 2.5 Take the square root of each side: x = {-1.58113883, 1.58113883}Solution
x = {-1.58113883, 1.58113883, -1.58113883, 1.58113883}
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