how do I solve 5x^2+5x-60=0 using the quadratic formula?
I would reduce it first to
x^2 + x - 12 = 0
then:
a = 1, b = 1, c = -12
so...
x = (-1 ± √(1 - 4(1)(-12))/2
= (-1 ± √49)/2
= (-1 ± 7)/2
= 3 or -4
well first divide both sides by 5
1 x^2 + 1 x - 12 = 0
x = [ -1 +/- sqrt( 1 -4(1)(-12) ] / 2
x = [ -1 +/- sqrt(49)] /2
x = [ -1 +/- 7 ]/2
x = 3 or x = -4
CHECK
5*9 + 5*3 - 60 = ?
45 +15 - 60 = 0 sure enough
To solve the quadratic equation 5x^2 + 5x - 60 = 0 using the quadratic formula, you'll need to follow these steps:
1. Identify the values of a, b, and c from the equation. In this case, a = 5, b = 5, and c = -60.
2. Plug the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
3. Substitute the values we have:
x = (-(5) ± √((5)^2 - 4(5)(-60))) / (2(5))
4. Simplify the equation:
x = (-5 ± √(25 + 1200)) / 10
x = (-5 ± √1225) / 10
5. Take the square root of 1225:
x = (-5 ± 35) / 10
6. Solve for both values of x:
x₁ = (-5 + 35) / 10 = 30/10 = 3
x₂ = (-5 - 35) / 10 = -40/10 = -4
So, the two solutions to the quadratic equation 5x^2 + 5x - 60 = 0 are x = 3 and x = -4.