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Simplifying 4x2 = 5x + -1 Reorder the terms: 4x2 = -1 + 5x Solving 4x2 = -1 + 5x Solving for variable 'x'. Reorder the terms: 1 + -5x + 4x2 = -1 + 5x + 1 + -5x Reorder the terms: 1 + -5x + 4x2 = -1 + 1 + 5x + -5x Combine like terms: -1 + 1 = 0 1 + -5x + 4x2 = 0 + 5x + -5x 1 + -5x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 1 + -5x + 4x2 = 0 Factor a trinomial. (1 + -4x)(1 + -1x) = 0Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0.25, 1}
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