How do you solve the quadratic equation
7x^2-5=0
7x^2 = 5
x^2 = 5/7
x = √(5/7)
Thank you for taking the time to help me out
To solve the quadratic equation 7x^2 - 5 = 0, you can use the quadratic formula. The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, the coefficients are:
a = 7, b = 0, and c = -5
Now, substitute these values into the quadratic formula:
x = (-(0) ± √((0)^2 - 4(7)(-5))) / (2(7))
Simplifying further:
x = (± √(0 - (-140))) / 14
x = (± √(140)) / 14
Now, take the square root of 140:
√(140) = 2√35
Therefore, the solutions to the equation 7x^2 - 5 = 0 are:
x = (2√35) / 14 and x = (-2√35) / 14
Simplifying further, we get:
x = √35 / 7 and x = -√35 / 7