Solve x² = 5 - x using the quadratic formula. what are the values of x?

Solution:

Given that:

x² = 5 - x 

It can be written in arranged form as:

x² + x - 5 = 0

The formula for the standard form of quadratic equation ax² + bx + c = 0 is written as

x = [−b ± √(b² − 4ac)] / 2a

From the given equation we know that

a = 1

b = 1

c = -5

Substituting it in the formula

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

x = [ -1 ± √{1 + 20} ] / 2

By further calculation

x = [ -1 ± √21 ] / 2

Therefore, the values of x are [-1 + √21] / 2 and [ -1 - √21 ] / 2.

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Solve x² = 5 - x using the quadratic formula. what are the values of x?

Summary:

By solving x² = 5 - x using the quadratic formula, the values of x are [-1 + √21] / 2 and [ -1 - √21 ] / 2.