x^2-5x=14 solve for x

Given the equation:

x^2 - 5x = 14

Can be written as,

x^2 - 5x - 14

Solve for x.

Solution:

In order to solve for the roots of an equation, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is -5 and when multiplied, the answer is -7. Hence, if we are unable to find the number, we will use the quadratic formula.

The factors that satisfy the equation are,

( x - 7 ) ( x + 2 )

In order to check if the equation is true, we simply need to apply the FOIL Method. Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation.

To clearly see how it works, here's a step by step solution.

= (x)(x)
=x^2
First term of the first equation multiplied to the first term of the second equation.

=(x)(2)
= 2x
First term of the first equation multiplied to the last term of the second equation.

=(x)(-7)
=-7x
Last term of the first equation multiplied to the first term of the second equation.

=(-7)(2)
= -14
Last term of the first equation multiplied to the fast term of the second equation.

= x^2 + 2x - 7x - 14
= x^2 - 5x -14

Since we've proven that the factors are true, we must equate them to 0 and solve for x.

x -7 = 0

x + 2 = 0

Transpose -7 and 2 to the opposite sides of the equation, hence it must be taken to note that in transposing a number, the sign changes.

x = 7

x = -2

Final answer:
x = 7

x = -2