Question

What are the exact solutions of x2 − 5x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a

Answer 1

Answer:

$x = \frac{5 + \sqrt{53}}{2}$  or  $x = \frac{5 - \sqrt{53}}{2}$

Step-by-step explanation:

Given

$x^2 - 5x - 7 = 0$

Required

Solve for x using:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

First, we need to identify a, b and c

The general form of a quadratic equation is:

$ax^2 + bx + c = 0$

So, by comparison with $x^2 - 5x - 7 = 0$

$a = 1$     $b = -5$      $c = -7$

Substitute these values of a, b and c in

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-5) \± \sqrt{(-5)^2 - 4 * 1 * -7}}{2 * 1}$

$x = \frac{5 \± \sqrt{25 +28}}{2}$

$x = \frac{5 \± \sqrt{53}}{2}$

Split the expression to two

$x = \frac{5 + \sqrt{53}}{2}$  or  $x = \frac{5 - \sqrt{53}}{2}$

To solve further in decimal form, we have

$x = \frac{5 + 7.28}{2}$  or  $x = \frac{5 - 7.28}{2}$

$x = \frac{12.28}{2}$  or  $x = \frac{-2.28}{2}$

$x = 6.14$ or $x = -1.14$