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Simplifying (5x2 + x)(5x2 + x) = 0 Reorder the terms: (x + 5x2)(5x2 + x) = 0 Reorder the terms: (x + 5x2)(x + 5x2) = 0 Multiply (x + 5x2) * (x + 5x2) (x(x + 5x2) + 5x2 * (x + 5x2)) = 0 ((x * x + 5x2 * x) + 5x2 * (x + 5x2)) = 0 ((x2 + 5x3) + 5x2 * (x + 5x2)) = 0 (x2 + 5x3 + (x * 5x2 + 5x2 * 5x2)) = 0 (x2 + 5x3 + (5x3 + 25x4)) = 0 Combine like terms: 5x3 + 5x3 = 10x3 (x2 + 10x3 + 25x4) = 0 Solving x2 + 10x3 + 25x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(1 + 10x + 25x2) = 0 Factor a trinomial. x2((1 + 5x)(1 + 5x)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2Subproblem 3
Set the factor '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2Solution
x = {0, -0.2, -0.2}
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