Final answer:
The equation x² = 5 - x, when rearranged into standard form x² + x - 5 = 0 and solved using the quadratic formula, yields two solutions: x = (-1 + √21) / 2 and x = (-1 - √21) / 2.
Step-by-step explanation:
To solve the given quadratic equation x² = 5 - x using the quadratic formula, we should first rearrange it into the standard quadratic form ax² + bx + c = 0. We can do this by adding x to both sides of the original equation, resulting in x² + x - 5 = 0. Now we have a = 1, b = 1, and c = -5. Applying the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a), we can calculate the two possible values for x.
Substituting our values into the formula gives us:
x = (-(1) ± √((1)² - 4(1)(-5))) / (2(1))
That simplifies to:
x = (-1 ± √(1 + 20)) / 2
x = (-1 ± √21) / 2
This yields two solutions for x:
Therefore, the equation x² = 5 - x has two solutions, which are the values found above using the quadratic formula.