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

`x = (5 + √(53))/(2)` or
`x = (5 - √(53))/(2)`

Explanation:

Given

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

Required

Solve for x using:

`x = (-b \± √(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 = (-b \± √(b^2 - 4ac))/(2a)`

`x = (-(-5) \± √((-5)^2 - 4 * 1 * -7))/(2 * 1)`

`x = (5 \± √(25 +28))/(2)`

`x = (5 \± √(53))/(2)`

Split the expression to two

`x = (5 + √(53))/(2)` or
`x = (5 - √(53))/(2)`

To solve further in decimal form, we have

`x = (5 + 7.28)/(2)` or
`x = (5 - 7.28)/(2)`

`x = (12.28)/(2)` or
`x = (-2.28)/(2)`

`x = 6.14` or
`x = -1.14`