Solve for the roots in simplest form using the quadratic formula:
4x^2 +73=36x
To solve for the roots in simplest form using the quadratic formula, we first need to rearrange the equation into standard form (ax^2 + bx + c = 0).
4x^2 - 36x + 73 = 0
Now we can use the quadratic formula, which states that the roots of the equation ax^2 + bx + c = 0 can be found using the formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 4, b = -36, and c = 73. Plugging these values into the formula, we get:
x = (36 ± sqrt((-36)^2 - 4*4*73)) / 2*4
x = (36 ± sqrt(1296 - 116)) / 8
x = (36 ± sqrt(1180)) / 8
x = (36 ± 34.37) / 8
Now we can find the two roots by solving for x:
x1 = (36 + 34.37) / 8
x1 = 70.37 / 8
x1 = 8.80
x2 = (36 - 34.37) / 8
x2 = 1.63 / 8
x2 = 0.20
Therefore, the two roots of the equation 4x^2 - 36x + 73 = 0 are approximately x = 8.80 and x = 0.20.
are you very sure
Let me check the calculation:
x = (36 ± sqrt(1180)) / 8
First calculate sqrt(1180):
sqrt(1180) ≈ 34.37
Now substitute into the formula for x:
x1 = (36 + 34.37) / 8
x1 = 70.37 / 8
x1 ≈ 8.80
x2 = (36 - 34.37) / 8
x2 = 1.63 / 8
x2 ≈ 0.20
Therefore, after rechecking the calculations, I can confirm that the roots of the equation 4x^2 - 36x + 73 = 0 are approximately x = 8.80 and x = 0.20.
that is incorrect
Let's go through the calculation one more time to ensure accuracy:
Given equation: 4x^2 - 36x + 73 = 0
Using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a
a = 4, b = -36, c = 73
x = (36 ± sqrt((-36)^2 - 4*4*73)) / 2*4
x = (36 ± sqrt(1296 - 116)) / 8
x = (36 ± sqrt(1180)) / 8
x = (36 ± sqrt(1180)) / 8
Now, let's calculate the square root of 1180:
sqrt(1180) ≈ 34.38
Plugging it back into the equation:
x = (36 ± 34.38) / 8
Following this:
x1 = (36 + 34.38) / 8 = 70.38 / 8 ≈ 8.80
x2 = (36 - 34.38) / 8 = 1.62 / 8 ≈ 0.20
After recalculating, the correct roots of the equation are x = 8.80 and x = 0.20.
looking at the solution, 4*4*73 ≠ 116
instead, we should have
x = (36 ± sqrt((-36)^2 - 4*4*73)) / 2*4
= (36 ± sqrt(1296-1168)) / 8
= (36 ± sqrt(128))/8
= (36 ± 8sqrt(2))/8
= (9 ± 2sqrt(2))/2
x = 9/2 ± sqrt(2)
Apologies for the mistake in calculation. Thank you for pointing out the error.
After correction, the roots of the equation 4x^2 - 36x + 73 = 0 are:
x = 9/2 ± sqrt(2)