Identify Coefficients: Step Title: Identify the Coefficients Concise Step Description: Identify the coefficients of the quadratic equation, which are the numbers in front of the variables. In this case, the coefficients are -64, -4, and -3. Step Calculation: Coefficients are -64, -4, -3 Step Output: Coefficients: -64, -4, -3Use Quadratic Formula: Step Title: Use the Quadratic Formula Concise Step Description: Since factoring might be difficult, use the quadratic formula to find the roots of the equation. The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the equation ax² + bx + c = 0. Step Calculation: For the equation -64c² - 4c - 3 = 0, a = -64, b = -4, and c = -3. Plugging these into the quadratic formula gives us: c = (-(-4) ± √((-4)² - 4(-64)(-3))) / (2(-64)) c = (4 ± √(16 - 768)) / (-128) c = (4 ± √(-752)) / (-128) Since the discriminant (the value under the square root) is negative, this equation has no real solutions. Step Output: No real solutions

Algebra 2

Factor polynomials

Full solution

-64 c^{2}-4 c-3=0

Identify Coefficients: Step Title: Identify the Coefficients $\newline$ Concise Step Description: Identify the coefficients of the quadratic equation, which are the numbers in front of the variables. In this case, the coefficients are $-64$ , $-4$ , and $-3$ . $\newline$ Step Calculation: Coefficients are $-64$ , $-4$ , $-3$ $\newline$ Step Output: Coefficients: $-64$ , $-4$ , $-3$
Use Quadratic Formula: Step Title: Use the Quadratic Formula $\newline$ Concise Step Description: Since factoring might be difficult, use the quadratic formula to find the roots of the equation. The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a$ , $b$ , and $c$ are the coefficients of the equation $ax^2 + bx + c = 0$ . $\newline$ Step Calculation: For the equation $-64c^2 - 4c - 3 = 0$ , $a = -64$ , $b = -4$ , and $c = -3$ . Plugging these into the quadratic formula gives us: $\newline$ $c = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(-64)(-3)}}{2(-64)}$ $\newline$ $a$ $0$ $\newline$ $a$ $1$ $\newline$ Since the discriminant (the value under the square root) is negative, this equation has no real solutions. $\newline$ Step Output: No real solutions