What are the solutions of x² = -5x + 8?

Solution:

A quadratic equation is represented as ax² + bx + c = 0 where a ≠ 0. The degree of a quadratic equation is equal to 2.

Given: x² = -5x + 8

x² = -5x + 8 can be witten as  x² + 5x - 8 = 0 in standard form.

sum = 5 and product = - 8

There are no two factors found.

Hence, we will use quadratic formula. 

The quadratic formula is given by

x = (-b ± √ (b² - 4ac)) / 2a

We know that coefficient of x²  is a, coefficient of x is b and the constant is c.

For the given equation x² + 5x - 8 = 0 ,

We have, a = 1, b = 5 and c = -8

Using the quadratic formula, we get,

⇒ x = -5 ± √ (5² - 4(1) ( - 8)) / 2(1) 

⇒ x = -5 ± √ 25 - (- 32) / 2(1) 

⇒ x = (-5 ± √57) / 2

Hence, we have two solutions:

x = (-5 - √57) / 2 and, x = (-5 + √57) / 2

We can use Online Quadratic Equation Calculator to solve the quadratic equation.

Thus, the solutions are (-5 - √57) / 2 and (-5 + √57) / 2 for the equation x² = -5 x + 8 .

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What are the solutions of x² = -5x + 8?

Summary:

The solutions that satisfies the equation x² = -5 x + 8 are (-5 - √57) / 2 and (-5 + √57) / 2.