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Simplifying (5x2 + -3)(5x2 + -3) = 0 Reorder the terms: (-3 + 5x2)(5x2 + -3) = 0 Reorder the terms: (-3 + 5x2)(-3 + 5x2) = 0 Multiply (-3 + 5x2) * (-3 + 5x2) (-3(-3 + 5x2) + 5x2 * (-3 + 5x2)) = 0 ((-3 * -3 + 5x2 * -3) + 5x2 * (-3 + 5x2)) = 0 ((9 + -15x2) + 5x2 * (-3 + 5x2)) = 0 (9 + -15x2 + (-3 * 5x2 + 5x2 * 5x2)) = 0 (9 + -15x2 + (-15x2 + 25x4)) = 0 Combine like terms: -15x2 + -15x2 = -30x2 (9 + -30x2 + 25x4) = 0 Solving 9 + -30x2 + 25x4 = 0 Solving for variable 'x'. Factor a trinomial. (3 + -5x2)(3 + -5x2) = 0Subproblem 1
Set the factor '(3 + -5x2)' equal to zero and attempt to solve: Simplifying 3 + -5x2 = 0 Solving 3 + -5x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x2 = 0 + -3 -5x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5x2 = -3 Divide each side by '-5'. x2 = 0.6 Simplifying x2 = 0.6 Take the square root of each side: x = {-0.774596669, 0.774596669}Subproblem 2
Set the factor '(3 + -5x2)' equal to zero and attempt to solve: Simplifying 3 + -5x2 = 0 Solving 3 + -5x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x2 = 0 + -3 -5x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5x2 = -3 Divide each side by '-5'. x2 = 0.6 Simplifying x2 = 0.6 Take the square root of each side: x = {-0.774596669, 0.774596669}Solution
x = {-0.774596669, 0.774596669, -0.774596669, 0.774596669}
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