Which are the solutions of x2 = –11x + 4?

Given the equation:

x^2 = - 11x + 4

Determine the solutions.

Solution:

In order to determine the solution of the equation, we must first transpose -11x and 4 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.

x^2 = -11x + 4

= x^2 + 11x - 4

a = 1

b = 11

c = -4

In order to solve for the roots or zeros 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 11, and when multiplied, the answer is -4. Hence, if we are unable to find the number, we will use the quadratic formula.

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a

x = −(11) ± √((11)^2 − 4(1)(-4))/2(1)

x = −(11) ± √(121 + 16)/2

x = −(11) ± √(137)/2

x = −(11) ± 11.7/2

Solve for +- separately.

x = -11 + 11.7/2
x = .7/2
x = 0.35

x = -11 - 11.7/2
x = -22.7/2
x = -11.35

Final answer:

x = 0.35

x = -11.35