Question

Fiona is completing the square to solve the polynomial equation.

x2 – 4x + 1 = 0

What should be her first step?

Answer 1

Use the quadratic formula

Explanation:

x^{2}-4x+1=0

a=1

b=-4

c=1

2 Simplify

Evaluate the exponent

Multiply the numbers

Subtract the numbers

Evaluate the square root

Multiply the numbers

3 Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x=\frac{4+2\sqrt{3}}{2}

x=\frac{4-2\sqrt{3}}{2}

4 Solve

Rearrange and isolate the variable to find each solution

x=2+\sqrt{3}

x=2-\sqrt{3}

= x=2±sqrt(3)