# How do you solve the quadratic using the quadratic formula given #3a^2=6a-3#?

Formula Problem a 3 b -6 c 3 x a

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To solve the quadratic equation (3a^2 = 6a - 3) using the quadratic formula, we first rearrange the equation into the standard form (ax^2 + bx + c = 0), where (a), (b), and (c) are constants.

[3a^2 - 6a + 3 = 0]

Comparing this equation with the standard form, we have (a = 3), (b = -6), and (c = 3).

Now, we can apply the quadratic formula, which states that for a quadratic equation (ax^2 + bx + c = 0), the solutions for (x) are given by:

[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}]

Substituting the values of (a), (b), and (c) into the quadratic formula, we get:

[a = 3, \quad b = -6, \quad c = 3]

[x = \frac{{-(-6) \pm \sqrt{{(-6)^2 - 4 \cdot 3 \cdot 3}}}}{{2 \cdot 3}}]

[x = \frac{{6 \pm \sqrt{{36 - 36}}}}{6}]

[x = \frac{{6 \pm \sqrt{0}}}{6}]

Since the discriminant ((b^2 - 4ac)) is zero, we have a repeated real root.

[x = \frac{{6 \pm 0}}{6}]

So, the solutions to the quadratic equation (3a^2 = 6a - 3) are:

[x = \frac{6}{6} = 1]

Therefore, the only solution to the equation is (a = 1).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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