How to factorize x^2 + 5x - 36

How can we factor $$x^2 + 5x - 36$$?

Answer: $$x^2+5x-36=(x+9)(x-4)$$

The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Find a pair of factors of $$36$$ which differ by $$5$$.

As you can see above, the pair (4, 9) works because $$9$$ x $$4=36$$ and $$9 - 4 =5$$

So, the answer is $$x^2+5x-36=(x+9)(x-4)$$

You can also factorize by solving the quadratic equation

The equation x² + 5x - 36 = 0 has 2 real roots when solved:

x₁ = -9 and x₂ = 4

Thus, $$x^2+5x-36=(x+9)(x-4)$$

Solving the equation

An equation like ax² + bx + c = 0, can be solved by using the quadratic equation formula:

x = -b ± √b² - 4ac2a

or

x = -b ± √Δ2a

Where

Δ (Delta) = b² - 4ac

See step-by-step solution below:

Identify the coefficients

a = 1, b = 5 and c = -36

Evaluate the value of Delta

Δ = b² - 4ac

Δ = 5² - 4.1.(-36) = 25 - 4.(-36)

Δ = 25 - (-144) = 169

Plug the values of a, b and Δ (the discriminant) into the Bhaskara formula

x = -b ± √Δ2a

x = -5 ± √1692.1

x = -5 ± √1692 (general solution)

As we can see above, the discriminant (Δ) of this equation is positive (Δ > 0) meaning that there are two real roots (two solutions), x₁ and x₂.

To find x₁, we just choose the negative sign before the square root of delta. So,

x₁ = -5 -1692 = -5 - 132 = -182 = -9

To find x₂, we just choose the positive sign before the square root of delta. So,

x₂ = -5 +1692 = -5 + 132 = 82 = 4

S = {-9, 4}

By coolconversion.com