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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 = 0 (-9 + 0 + 25x4) = 0 (-9 + 25x4) = 0 Solving -9 + 25x4 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 25x4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 25x4 = 0 + 9 25x4 = 0 + 9 Combine like terms: 0 + 9 = 9 25x4 = 9 Divide each side by '25'. x4 = 0.36 Simplifying x4 = 0.36 Reorder the terms: -0.36 + x4 = 0.36 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 -0.36 + x4 = 0.00 Factor a difference between two squares. (0.6 + x2)(-0.6 + x2) = 0.00Subproblem 1
Set the factor '(0.6 + x2)' equal to zero and attempt to solve: Simplifying 0.6 + x2 = 0 Solving 0.6 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x2 = 0 + -0.6 x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 x2 = -0.6 Simplifying x2 = -0.6 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-0.6 + x2)' equal to zero and attempt to solve: Simplifying -0.6 + x2 = 0 Solving -0.6 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x2 = 0 + 0.6 x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 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}
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