Give exact and approximate solutions tto three decimal places
x^2-7x+9=0
Look over other solution and see if you can figure this one out now.
To find the exact and approximate solutions to the equation x^2 - 7x + 9 = 0, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the quadratic equation with the general form ax^2 + bx + c = 0, we can identify the coefficients as follows:
a = 1, b = -7, c = 9
Substituting these values into the quadratic formula:
x = (7 ± √((-7)^2 - 4(1)(9))) / (2(1))
Simplifying further:
x = (7 ± √(49 - 36)) / 2
x = (7 ± √(13)) / 2
So the exact solutions to the equation are:
x = (7 + √(13)) / 2
and
x = (7 - √(13)) / 2
To obtain the approximate solutions to three decimal places, we will plug in the numerical values for √(13) and simplify:
√(13) ≈ 3.605
Therefore, the approximate solutions to three decimal places are:
x ≈ (7 + 3.605) / 2 ≈ 5.303
x ≈ (7 - 3.605) / 2 ≈ 1.697