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# Find the real solutions of the equation by graphing. x^{2} + 2x + 2 = 0

**Solution:**

Given, x^{2} + 2x + 2 = 0

We have to find the real solutions of the equation by graphing.

By substituting the value of x for x coordinates, we get the values of y coordinates.

1) When x = 0

⇒ y = x^{2} + 2x + 2

⇒ y = (0)^{2} + 2(0) + 2

⇒ y = 2

2) when x = 1

⇒ y = x^{2} + 2x + 2

⇒ y = (1)^{2} + 2(1) + 2

⇒ y = 1 + 2 + 2

⇒ y = 5

3) When x = 2

⇒ y = x^{2} + 2x + 2

⇒ y = (2)^{2} + 2(2) + 2

⇒ y = 4 + 4 + 2

⇒ y = 10

4) When x = -2

⇒ y = x^{2} + 2x + 2

⇒ y = (-2)^{2} + 2(-2) + 2

⇒ y = 4 - 4 + 2

⇒ y = 2

The intercepts of the x-axis are the solutions of the equation.

a) If the graph touches the x-axis at two points, there are two real solutions for the equation.

b) If the graph touches the x-axis at one point, there is only one real solution for the equation.

c) If the graph does not touch the x-axis, there are no real solutions.

Since the graph has no x-intercepts, there is no real solution.

Therefore, the given quadratic equation has no real solution.

## Find the real solutions of the equation by graphing. x^{2} + 2x + 2 = 0

**Summary:**

By graphing, the quadratic equation x^{2} + 2x + 2 = 0 has no real solution.

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