Question

t^2+2t=t+3
Solve th following quadratic equation by completing the square method.

Answer 1

Answer:

Hope the answer helped you...

Answer 2

Concept

Completing the square is one of the ways by which we can solve a quadratic equation. In this method, the given equation is adjusted to make it fit into the formula of (a+b)^2.

Given

a quadratic equation t^2+2t=t+3

Find

we need to solve the given quadratic equation by using completing the square method.

Solution

We have

t^2 + 2t = t + 3

⇒ t^2 + 2t - t - 3 =0

⇒ t^2 + t - 3 =0

we know that (a+b)^2 = a^2 + b^2 + 2ab

Here, a^2 = t^2

thus, a = t

2ab = t

⇒ b = 1/2

Therefore b^2 = 1/4

Thus, the equation can be written as

t^2 + 2(1/2)t + 1/4 -1/4 - 3 = 0

⇒ (t + 1/2)^2 = 13/4

⇒ t + 1/2 = sqrt(13)/2

⇒ t = (√13 - 1)/2

Thus, t = (√13 - 1)/2 is the solution to the equation t^2+2t=t+3.

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