Algebra

x^2+6x-5 solve for x

Step-by-step solution with explanation

Final Answer

and

Step-by-step solution

1

Set the equation equal to zero

To solve for x, we need the equation set to zero. It already is, so we're ready to apply the quadratic formula.
2

Identify a, b, and c values

In any quadratic , we label the coefficients. Here a is 1, b is 6, and c is -5.
3

Write the quadratic formula

The quadratic formula always works for any quadratic equation. We'll plug in our a, b, and c values next.
4

Calculate the discriminant

The discriminant tells us how many real solutions exist. Since 56 is positive, we'll get two real solutions.
5

Substitute values into the formula

We plug a = 1, b = 6, and c = -5 into the formula. Now we simplify the square root.
6

Simplify the square root

We factor 56 into 4 × 14, then pull the perfect square (4) out as a 2. This gives us a cleaner form.
7

Simplify and write both solutions

We divide both -6 and by 2. This gives us two final answers: and .

Understanding this problem

Learning Insight

The quadratic formula works because it completes the square for you behind the scenes. Every quadratic has exactly two solutions (counting multiplicity) — the ± sign is what produces both of them. When the discriminant is positive but not a perfect square, the answers are irrational numbers like these.

Quick Tip

Always simplify first by pulling out perfect square factors. It makes the final division cleaner and helps you spot if further simplification is possible.

Common Mistake

Students often forget that c = -5 is negative when computing , writing instead of . Double-check the sign of c every time.