What are the solutions of the quadratic equation below?
4x2 - 30x + 45 = 0
Online, "^" indicates an exponent, x^2 = x squared.
Try to factor the equation
Consider two factors that give the final term (9*5, 15*3, 45*1). Do the same with the first term (2*2, 4*1). Is there any combination of the two that will add to 30?
All I can get for the middle term are -27, - 29, -63 or -41. Do you have a typo in your equation?
To find the solutions of the quadratic equation 4x^2 - 30x + 45 = 0, we can use the quadratic formula. The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.
In this case, a = 4, b = -30, and c = 45.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Substituting the values into the formula, we get:
x = (30 ± √((-30)^2 - 4 * 4 * 45)) / 2 * 4
Simplifying further:
x = (30 ± √(900 - 720)) / 8
x = (30 ± √180) / 8
Now, let's simplify the square root of 180:
√180 = √(36 * 5) = 6√5
Therefore, the solutions of the quadratic equation are:
x = (30 + 6√5) / 8
x = (30 - 6√5) / 8
Note that these solutions can be further simplified if needed.