Solve the quadratic by factoring.
2x^2+4=-5x+1

see explanation

Step-by-step explanation:

Given

2x² + 4 = - 5x + 1

To express in standard form subtract - 5x + 1 from both sides

2x² + 5x + 3 = 0 ← in standard form

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 + 3 = 6 and sum = + 5

The factors are + 2 and + 3

Use these factors to split the x- term

2x² + 2x + 3x + 3 = 0 ( factor the first/second and third/fourth terms )

2x(x + 1) + 3(x + 1) = 0 ← factor out (x + 1)

(x + 1)(2x + 3) = 0

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = -

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.