4x² +2x-1=0

To solve the equation 4x² + 2x - 1 = 0, you can use the quadratic formula or factorization.

Using the quadratic formula: The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). From the equation 4x² + 2x - 1 = 0, we have a = 4, b = 2, and c = -1. Substituting the values into the quadratic formula, we have: x = (-2 ± √((2)² - 4(4)(-1))) / (2(4)) x = (-2 ± √(4 + 16)) / 8 x = (-2 ± √20) / 8 x = (-2 ± √4∙5) / 8 x = (-2 ± 2√5) / 8 Simplifying further gives: x = (-1 ± √5) / 4

So the solutions to the equation 4x² + 2x - 1 = 0 are: x = (-1 + √5) / 4 x = (-1 - √5) / 4

Using factorization: We need to find two numbers whose product is ac (4*-1 = -4) and whose sum is b (2). In this case, the numbers are 4 and -1. Therefore, we rewrite the equation as: 4x² + 4x - 5x - 1 = 0 Grouping the terms, we get: (4x² + 4x) - (5x + 1) = 0 Factoring out the common terms from each group: 4x(x + 1) - 1(5x + 1) = 0 Simplifying further: 4x(x + 1) - (5x + 1) = 0 Distributing the negative sign: 4x(x + 1) - 5x - 1 = 0 Rearranging the terms: 4x(x + 1) - (5x + 1) = 0 Factoring the quadratic equation: (4x - 1)(x + 1) = 0 Setting each factor to zero and solving for x: 4x - 1 = 0 or x + 1 = 0 4x = 1 or x = -1 x = 1/4 or x = -1

So the solutions to the equation 4x² + 2x - 1 = 0 are: x = 1/4 x = -1