Solve for v. v^(2)-6v=-91

Question

Bytelearn · Accepted Answer

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 1, -6, and 91. Step Calculation: Coefficients are 1, -6, 91.Find Factors: Step Title: Find the Factors Concise Step Description: Find two numbers that multiply to 91 (the last term) and add to -6 (the coefficient of the middle term). Step Calculation: Factors of 91 that add up to -6 are -1 and -91, -7 and -13. However, none of these pairs add up to -6, which means the quadratic equation cannot be factored using integers.Factor or Use Formula: Step Title: Attempt to Factor or Use the Quadratic Formula Concise Step Description: Since the quadratic equation cannot be factored using integers, we will use the quadratic formula to find the roots. Step Calculation: The quadratic formula is v = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -6, and c = 91. Plugging these values in, we get v = (6 ± √((-6)^2 - 4(1)(91))) / (2(1)) = (6 ± √(36 - 364)) / 2 = (6 ± √(-328)) / 2. Since we have a negative number under the square root, the solutions will be complex numbers.Calculate Discriminant: Step Title: Calculate the Discriminant Concise Step Description: Calculate the discriminant to determine the nature of the roots. Step Calculation: The discriminant is b^2 - 4ac = (-6)^2 - 4(1)(91) = 36 - 364 = -328. Since the discriminant is negative, the equation has two complex solutions.

Solve for $v$ . $\newline$ $v^{2}-6 v=-91$

Full solution

More problems from Factor polynomials

Related topics

Solve for vvv.\newlinev2−6v=−91 v^{2}-6 v=-91 v2−6v=−91

Solve for $v$ . $\newline$ $v^{2}-6 v=-91$