How do you solve #5v^2-7v=1# using the quadratic formula?

Question

Isaiah Anthony · Accepted Answer

Move everything so all terms are on one side of the = sign, and solve for zero using the Quadratic Formula. There are two answers: v=#(7\pmsqrt(69))/10#.

Subtract 1 from both sides so you have #5v^2 - 7v - 1=0#. The "standard form" of a quadratic is #ax^2 + bx + c#, so first we have to identify a, b, and c in your equation: a=5, b= -7, and c= -1. The quadratic formula is #(-b\pmsqrt(b^2 - 4ac))/(2a)#. Plugging in your values, we get #(-7 \pm sqrt(69))/(2*5)#, or #v=(7\pmsqrt(69))/10#. It looks a little funny, but you can't simplify it any more. You can check the answer by graphing the function on your calculator and asking for the function value at these points. After graphing, hit 2nd, "Calc", "Value" on your TI, and type in either #(7+sqrt(69))/10# or #(7-sqrt(69))/10#, and you'll get that #y = 0#.

Isaiah Anthony · Answer

undefined To solve the quadratic equation 5v^2 - 7v = 1 using the quadratic formula, first, identify the coefficients a, b, and c:

a = 5
b = -7
c = 1

Now, plug these values into the quadratic formula:

v = (-b ± √(b^2 - 4ac)) / (2a)

Substitute the values of a, b, and c:

v = (-(−7) ± √((-7)^2 - 4(5)(1))) / (2(5))

Simplify the expression:

v = (7 ± √(49 - 20)) / 10
v = (7 ± √29) / 10

So, the solutions for the equation 5v^2 - 7v = 1 are:

v = (7 + √29) / 10
v = (7 - √29) / 10

Savannah Anderson · Answer

undefined To solve the quadratic equation $5v^2 - 7v = 1$ using the quadratic formula, first identify the coefficients $a$, $b$, and $c$ in the general quadratic equation $av^2 + bv + c = 0$.

In this equation, $a = 5$, $b = -7$, and $c = -1$.

Now, substitute these values into the quadratic formula:

$$ v = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} $$

Substitute the values of $a$, $b$, and $c$:

$$ v = \frac{{-(-7) \pm \sqrt{{(-7)^2 - 4(5)(-1)}}}}{{2(5)}} $$

Simplify inside the square root:

$$ v = \frac{{7 \pm \sqrt{{49 + 20}}}}{{10}} $$
$$ v = \frac{{7 \pm \sqrt{{69}}}}{{10}} $$

So, the solutions to the equation $5v^2 - 7v = 1$ using the quadratic formula are:

$$ v = \frac{{7 + \sqrt{{69}}}}{{10}} $$ or $$ v = \frac{{7 - \sqrt{{69}}}}{{10}} $$