Identify Coefficients: Identify the coefficients of the quadratic equation. In the equation 6x^2 + 7x + 1 = 0, the coefficients are a = 6, b = 7, and c = 1. Apply Quadratic Formula: Apply the quadratic formula, x = (-b ± sqrt(b^2 - 4ac)) / (2a). Here, b^2 - 4ac = 7^2 - 4*6*1 = 49 - 24 = 25. Calculate Discriminant: Calculate the discriminant sqrt(b^2 - 4ac). sqrt(25) = 5. Solve for x: Solve for x using the positive and negative values of the square root. x = (-7 + 5) / (2*6) = -2 / 12 = -1/6, x = (-7 - 5) / (2*6) = -12 / 12 = -1.

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$6 x^{2}+7 x+1=0$

View step-by-step help

Home

Math Problems

Algebra 1

Add and subtract polynomials

Full solution

6 x^{2}+7 x+1=0

Identify Coefficients: Identify the coefficients of the quadratic equation. $\newline$ In the equation $6x^2 + 7x + 1 = 0$ , the coefficients are $a = 6$ , $b = 7$ , and $c = 1$ .
Apply Quadratic Formula: Apply the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . $\newline$ Here, $b^2 - 4ac = 7^2 - 4\cdot6\cdot1 = 49 - 24 = 25$ .
Calculate Discriminant: Calculate the discriminant $\sqrt{b^2 - 4ac}$ . $\sqrt{25} = 5$ .
Solve for x: Solve for x using the positive and negative values of the square root. $\newline$ $x = \frac{-7 + 5}{2\cdot6} = \frac{-2}{12} = -\frac{1}{6}$ , $\newline$ $x = \frac{-7 - 5}{2\cdot6} = \frac{-12}{12} = -1$ .