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## Use the quadratic formula to solve for x. 6x²-3x=1 Round your answer to the nearest hundredth. If there is more than one s

Question

Use the quadratic formula to solve for x.

6x²-3x=1

Round your answer to the nearest hundredth.

If there is more than one solution, separate them with commas.

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Mathematics
5 months
2021-08-24T12:13:27+00:00
2021-08-24T12:13:27+00:00 1 Answers
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## Answers ( )

If we know the quadratic formula, the quadratic formula is

x = [-b ± √(b²- 4ac)] / 2a

Gosh! So overwhelming! But let’s look at the composition of a quadratic equation:

ax² + bx + c = 0

And we have 6x² – 3x = 1. So, what do we do? We need to put this quadratic equation into an easy form to find the value of a, b, and c to plug in to the equation.

We can just minus one on both sides to get this:

6x² – 3x – 1 = 0

Is it in the form of ax² + bx + c? Yes! a = 6, b = -3, and c = -1. Now, all we have to do is plug it into the quadratic formula.

x = [-b ± √(b²- 4ac)] / 2a

x = [-(-3) ± √((-3)²- 4(6)(-1))] / 2(6)

[3 ± √(9- 4(6)(-1))] / 12

[3 ± √(9 + 24)] / 12

[3 ± √(33)] / 12

At this point, we should just use a calculator, and recognize we have two answers because of the plus-or-minus sign! (or this sign: ±)

[3 ± √(33)] / 12

1) [3 + √(33)] / 12 = 0.73 approximately

2) [3 – √(33)] / 12 = -0.23 approximately

So, x=0.73 and x= -0.23.