What are the solutions of the quadratic equation?

4x^2 - 9x - 9 = 0

Substitute the values a = 4 , b = - 9 , c = - 9 into the quadratic formula

x1/2 = [ - b +OR- sqroot( b ^ 2 - 4 a c ) ] / 2 a

x1/2 = [ - ( - 9 ) +OR- sqroot( ( - 9 ) ^ 2 - 4 * 4 * ( - 9 ) ) ] / 2 * 4

x1/2 = [ 9 +OR- sqroot( 81 - 4 * ( - 36) ) ] / 8

x1/2 = [ 9 +OR- sqrt ( 81 + 144 )] / 8

x1/2 = [ 9 +OR- sqrt ( 255 )] / 8

x1/2 = ( 9 +OR- 15 ) / 8

x1 = ( 9 + 15 ) / 8 = 24 / 8 = 3

x2 = ( 9 - 15 ) / 8 = - 6 / 8 = - 3 * 2 / ( 4 * 2 ) = - 3 / 4

The solutions are :

x = - 3 / 4 and x = 3

Ah, the quadratic equation! It's like a math rollercoaster with its ups and downs. Now let's get to finding those solutions and getting off this ride.

Using the trustworthy quadratic formula, we plug in the coefficients:

x = (-b ± √(b² - 4ac))/(2a)

In your case, a = 4, b = -9, and c = -9. Carefully crunching the numbers, we get:

x = (9 ± √((-9)² - 4 * 4 * -9))/(2 * 4)

x = (9 ± √(81 + 144))/(8)

x = (9 ± √(225))/(8)

x = (9 ± 15)/(8)

Now, let's branch out into two possibilities:

1. x = (9 + 15)/(8) = 24/8 = 3. There's one solution.

2. x = (9 - 15)/(8) = -6/8 = -3/4. And here's the second solution!

So, the solutions to your quadratic equation are x = 3 and x = -3/4. Keep those numbers close, they might come in handy in the math carnival!

To find the solutions of a quadratic equation, you can use the quadratic formula. The quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

For the equation 4x^2 - 9x - 9 = 0, we can identify the coefficients:

a = 4
b = -9
c = -9

Substituting these values into the quadratic formula, we have:

x = (9 ± √((-9)^2 - 4 * 4 * -9)) / (2 * 4)

Simplifying further:

x = (9 ± √(81 + 144)) / 8
x = (9 ± √(225)) / 8
x = (9 ± 15) / 8

So the two solutions are:

x₁ = (9 + 15) / 8 = 24 / 8 = 3
x₂ = (9 - 15) / 8 = -6 / 8 = -3/4

Therefore, the solutions to the quadratic equation 4x^2 - 9x - 9 = 0 are x = 3 and x = -3/4.

Thank you!

x= (9+-sqrt(81+4*4*9))/8

x= 1/2 +- 15/8