Add 5 to both sides: Add 5 to both sides of the equation to set it equal to zero. 4v^2 - 8v - 145 = -5 4v^2 - 8v - 145 + 5 = -5 + 5 4v^2 - 8v - 140 = 0Factor the quadratic equation: Factor the quadratic equation. To factor 4v^2 - 8v - 140, we need to find two numbers that multiply to 4 * -140 = -560 and add to -8. However, this quadratic does not factor nicely, so we will use the quadratic formula instead. The quadratic formula is v = (-b ± √(b^2 - 4ac)) / (2a), where a = 4, b = -8, and c = -140.Calculate the discriminant: Calculate the discriminant (b^2 - 4ac) of the quadratic formula. Discriminant = (-8)^2 - 4 * 4 * -140 Discriminant = 64 + 2240 Discriminant = 2304Calculate the two solutions: Calculate the two solutions using the quadratic formula. v = (-(-8) ± √2304) / (2 * 4) v = (8 ± √2304) / 8 v = (8 ± 48) / 8Solve for the first value: Solve for the two possible values of v. First solution: v = (8 + 48) / 8 v = 56 / 8 v = 7Solve for the second value: Solve for the second possible value of v. Second solution: v = (8 - 48) / 8 v = -40 / 8 v = -5

Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

4 v^{2}-8 v-145=-5

Add $5$ to both sides: Add $5$ to both sides of the equation to set it equal to zero. $\newline$ $4v^2 - 8v - 145 = -5$ $\newline$ $4v^2 - 8v - 145 + 5 = -5 + 5$ $\newline$ $4v^2 - 8v - 140 = 0$
Factor the quadratic equation: Factor the quadratic equation. $\newline$ To factor $4v^2 - 8v - 140$ , we need to find two numbers that multiply to $4 \times -140 = -560$ and add to $-8$ . $\newline$ However, this quadratic does not factor nicely, so we will use the quadratic formula instead. $\newline$ The quadratic formula is $v = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 4$ , $b = -8$ , and $c = -140$ .
Calculate the discriminant: Calculate the discriminant $b^2 - 4ac$ of the quadratic formula. $\newline$ Discriminant = $(-8)^2 - 4 \times 4 \times -140$ $\newline$ Discriminant = $64 + 2240$ $\newline$ Discriminant = $2304$
Calculate the two solutions: Calculate the two solutions using the quadratic formula. $\newline$ $v = \frac{-(-8) \pm \sqrt{2304}}{2 \times 4}$ $\newline$ $v = \frac{8 \pm \sqrt{2304}}{8}$ $\newline$ $v = \frac{8 \pm 48}{8}$
Solve for the first value: Solve for the two possible values of $v$ . $\newline$ First solution: $\newline$ $v = (8 + 48) / 8$ $\newline$ $v = 56 / 8$ $\newline$ $v = 7$
Solve for the second value: Solve for the second possible value of $v$ . $\newline$ Second solution: $\newline$ $v = (8 - 48) / 8$ $\newline$ $v = -40 / 8$ $\newline$ $v = -5$