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

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)

Answer:

Solutions to the Quadratic Equation x² + 2√2x - 6 = 0 are x = √2 (or 1.414) and x = -3√2 (or -4.243)

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