Solve for x
ax^2 - 2ax - 4 =0
just use the quadratic formula:
x = (2a±√(4a^2+16a))/(2a)
= (2a±2√(a^2+4a))/(2a)
= 1±√(a^2+4a)/a
or
= 1±√(1 + 4/a)
To solve the quadratic equation ax^2 - 2ax - 4 = 0, we can use the quadratic formula. The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the equation:
x = (-b ± √(b^2 - 4ac)) / (2a)
Now, let's apply the quadratic formula to solve the given equation ax^2 - 2ax - 4 = 0.
Comparing the given equation with the general quadratic equation form, we have:
a = a
b = -2a
c = -4
Substituting these values into the quadratic formula, we get:
x = (-(-2a) ± √((-2a)^2 - 4(a)(-4))) / (2a)
= (2a ± √(4a^2 + 16a)) / (2a)
= (2a ± √4a(a + 4)) / (2a)
= (2a ± 2√(a(a + 4))) / (2a)
Simplifying further, we have:
x = (a ± √(a(a + 4))) / a
= 1 ± √(a + 4) / √a
Hence, the solutions for x are:
x₁ = 1 + √(a + 4) / √a
x₂ = 1 - √(a + 4) / √a