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Simplifying (4x2 + 1) + (19x + 4) + (x2 + 7x) = 0 Reorder the terms: (1 + 4x2) + (19x + 4) + (x2 + 7x) = 0 Remove parenthesis around (1 + 4x2) 1 + 4x2 + (19x + 4) + (x2 + 7x) = 0 Reorder the terms: 1 + 4x2 + (4 + 19x) + (x2 + 7x) = 0 Remove parenthesis around (4 + 19x) 1 + 4x2 + 4 + 19x + (x2 + 7x) = 0 Reorder the terms: 1 + 4x2 + 4 + 19x + (7x + x2) = 0 Remove parenthesis around (7x + x2) 1 + 4x2 + 4 + 19x + 7x + x2 = 0 Reorder the terms: 1 + 4 + 19x + 7x + 4x2 + x2 = 0 Combine like terms: 1 + 4 = 5 5 + 19x + 7x + 4x2 + x2 = 0 Combine like terms: 19x + 7x = 26x 5 + 26x + 4x2 + x2 = 0 Combine like terms: 4x2 + x2 = 5x2 5 + 26x + 5x2 = 0 Solving 5 + 26x + 5x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + x)(1 + 5x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 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 = -0.2Solution
x = {-5, -0.2}
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