Nov 26, 2023

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Nov 26, 2023

To factorize the quadratic equation 2x^2 - 8x - 11 = 0, we need to find two binomials that multiply together to give the quadratic equation.

First, we multiply the coefficient of x^2 (2) with the constant term (-11), which gives us -22. We need to find two numbers that multiply to -22 and add up to the coefficient of x (-8).

The numbers that satisfy this condition are -11 and 2, since -11 * 2 = -22 and -11 + 2 = -9.

Now, we rewrite the middle term (-8x) using these two numbers:

2x^2 - 11x + 2x - 11 = 0

Next, we group the terms:

(2x^2 - 11x) + (2x - 11) = 0

Now, we factor out the common terms from each group:

x(2x - 11) + 1(2x - 11) = 0

We can see that (2x - 11) is common to both terms, so we can factor it out:

(2x - 11)(x + 1) = 0

Setting each factor equal to zero, we get:

2x - 11 = 0 or x + 1 = 0

Solving these equations, we find:

2x = 11 or x = -1

Dividing both sides of the first equation by 2, we get:

x = 11/2

Therefore, the solutions to the quadratic equation 2x^2 - 8x - 11 = 0 are x = 11/2 and x = -1.

First, we multiply the coefficient of x^2 (2) with the constant term (-11), which gives us -22. We need to find two numbers that multiply to -22 and add up to the coefficient of x (-8).

The numbers that satisfy this condition are -11 and 2, since -11 * 2 = -22 and -11 + 2 = -9.

Now, we rewrite the middle term (-8x) using these two numbers:

2x^2 - 11x + 2x - 11 = 0

Next, we group the terms:

(2x^2 - 11x) + (2x - 11) = 0

Now, we factor out the common terms from each group:

x(2x - 11) + 1(2x - 11) = 0

We can see that (2x - 11) is common to both terms, so we can factor it out:

(2x - 11)(x + 1) = 0

Setting each factor equal to zero, we get:

2x - 11 = 0 or x + 1 = 0

Solving these equations, we find:

2x = 11 or x = -1

Dividing both sides of the first equation by 2, we get:

x = 11/2

Therefore, the solutions to the quadratic equation 2x^2 - 8x - 11 = 0 are x = 11/2 and x = -1.

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