# Solve Each of the Following Quadratic Equations: x^2+2√2x−6=0

By BYJU'S Exam Prep

Updated on: October 17th, 2023

Solve each of the following quadratic equations: x2+2√2x−6=0

There are multiple methods which can be used to solve the quadratic equation x^2 + 2√2x – 6 = 0. Here are a few commonly used methods:
By substituting the values of a, b, and c in Quadratic Formula, x = (-b ± √(b^2 – 4ac)) / (2a), we can directly calculate the solutions for x.
Factoring can also be used. If the quadratic equation can be factored, you can factorize it into two binomial expressions set equal to zero, and then solve for x.
Completing the Squares can also be the method to get the deseried answer.

## Solve Each of the Following Quadratic Equations: x2+2√2x−6=0

Solution:

To solve the quadratic equation x2 + 2√2x – 6 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b2 – 4ac)) / (2a)

In this case, a = 1, b = 2√2, and c = -6. Let’s substitute these values into the quadratic formula and solve for x:

x = (-(2√2) ± √((2√2)2 – 4(1)(-6))) / (2(1))

Simplifying further:

x = (-2√2 ± √(8 + 24)) / 2

x = (-2√2 ± √32) / 2

x = -√2 ± 2√2

Now, let’s simplify the solutions:

x1 = -√2 + 2√2 = √2 (approx. 1.414)

x2 = -√2 – 2√2 = -3√2 (approx. -4.243)