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