Use the work shown to find the solutions of the quadratic equation.
x2 – x – StartFraction 3 Over 4 EndFraction = 0
x2 – x = StartFraction 3 Over 4 EndFraction
x2 – x + (StartFraction 1 Over 2 EndFraction) squared = StartFraction 3 Over 4 EndFraction + (StartFraction 1 Over 2 EndFraction) squared
x2 – x + StartFraction 1 Over 4 EndFraction = StartFraction 3 Over 4 EndFraction + StartFraction 1 Over 4 EndFraction
Which is a solution of x2 – x – StartFraction 3 Over 4 EndFraction = 0?
How about just typing it normally, such as
x^2 - x - 3/4 = 0
times 4 ...
4x^2 - 4x - 3 = 0 , it factors nicely
(2x - 3)(2x + 1) = 0
x = 3/2 or x = -1/2
now, re-enter the others and show why you are having difficulties.
The quadratic equation given is x^2 - x - 3/4 = 0.
To find the solutions, we can use the quadratic formula, which states that for any equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the given equation to the standard quadratic equation form, we have a = 1, b = -1, and c = -3/4.
Plugging these values into the quadratic formula, we have:
x = (-(−1) ± √((−1)^2 - 4(1)(−3/4))) / (2(1))
Simplifying further:
x = (1 ± √(1 + 3)) / 2
x = (1 ± √4) / 2
x = (1 ± 2) / 2
Taking the positive and negative solutions gives us:
x1 = (1 + 2) / 2 = 3/2
x2 = (1 - 2) / 2 = -1/2
Therefore, the solutions of the quadratic equation x^2 - x - 3/4 = 0 are x = 3/2 and x = -1/2.
To find the solutions of the quadratic equation x^2 - x - 3/4 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -1, and c = -3/4.
Plugging these values into the quadratic formula, we get:
x = (-(-1) ± √((-1)^2 - 4(1)(-3/4))) / (2(1))
Simplifying further:
x = (1 ± √(1 + 3)) / 2
x = (1 ± √(4)) / 2
x = (1 ± 2) / 2
Therefore, the solutions to the quadratic equation x^2 - x - 3/4 = 0 are:
x = (1 + 2) / 2 = 3/2
x = (1 - 2) / 2 = -1/2
So, the solutions are x = 3/2 and x = -1/2.