Question - Solving Quadratic Equations by Using the Quadratic Formula
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Solution:
The image you've provided is a little blurry, but it appears to show an algebraic expression that needs to be solved for x. The expression given is:3x^2 + 5x - 2 = 0This is a quadratic equation, which can be solved using several methods, such as factoring, completing the square, or using the quadratic formula. The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are coefficients, the solutions for x can be found using:x = (-b ± √(b^2 - 4ac)) / (2a)In this case, a = 3, b = 5, and c = -2. Plugging these values into the formula gives us:x = (-5 ± √(5^2 - 4*3*(-2))) / (2*3)x = (-5 ± √(25 + 24)) / 6x = (-5 ± √49) / 6x = (-5 ± 7) / 6This results in two possible solutions for x:x = (-5 + 7) / 6x = 2 / 6x = 1 / 3orx = (-5 - 7) / 6x = -12 / 6x = -2So the solutions for x are x = 1/3 or x = -2.
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