Using the quadratic formula to solve x² = 5 – x, what are the values of x?

The quadratic formula is the easiest way of solving quadratic equations especially when it is difficult to solve by the splitting of the middle term.

Answer: x =  [ -1 ± √21 ] / 2  are the solutions of the quadratic equation x² = 5 – x.

Let us use the quadratic formula to solve x² = 5 – x.

Explanation:

Let's write the equation in its standard form.

x² = 5 – x

x² + x - 5 = 0

a = 1, b = 1, c = -5          ------->   when we compare with the standard form of a quadratic expression ax² + bx + c = 0

By quadratic formula,

x = [ -b ± √(b² - 4ac) ] / 2a

x =  [ -(1) ± √{(1)² - 4(1)(-5)} ] / 2(1)

x =  [ -1 ± √{1 + 20} ] / 2 

x =  [ -1 ± √21 ] / 2 

values of x are: [-1 + √21] / 2 and  [ -1 - √21 ] / 2

Both the values of x are irrational numbers.

Thus, the solutions of the quadratic expression x² = 5 – x, using the quadratic formula are [ -1 ± √21 ] / 2.