Question
Find the roots
x1=94−231,x2=94+231
Alternative Form
x1≈−0.792837,x2≈1.681725
Evaluate
9x2−8x−12
To find the roots of the expression,set the expression equal to 0
9x2−8x−12=0
Substitute a=9,b=−8 and c=−12 into the quadratic formula x=2a−b±b2−4ac
x=2×98±(−8)2−4×9(−12)
Simplify the expression
x=188±(−8)2−4×9(−12)
Simplify the expression
More Steps

Evaluate
(−8)2−4×9(−12)
Multiply
More Steps

Multiply the terms
4×9(−12)
Rewrite the expression
−4×9×12
Multiply the terms
−432
(−8)2−(−432)
Rewrite the expression
82−(−432)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
82+432
Evaluate the power
64+432
Add the numbers
496
x=188±496
Simplify the radical expression
More Steps

Evaluate
496
Write the expression as a product where the root of one of the factors can be evaluated
16×31
Write the number in exponential form with the base of 4
42×31
The root of a product is equal to the product of the roots of each factor
42×31
Reduce the index of the radical and exponent with 2
431
x=188±431
Separate the equation into 2 possible cases
x=188+431x=188−431
Simplify the expression
More Steps

Evaluate
x=188+431
Divide the terms
More Steps

Evaluate
188+431
Rewrite the expression
182(4+231)
Cancel out the common factor 2
94+231
x=94+231
x=94+231x=188−431
Simplify the expression
More Steps

Evaluate
x=188−431
Divide the terms
More Steps

Evaluate
188−431
Rewrite the expression
182(4−231)
Cancel out the common factor 2
94−231
x=94−231
x=94+231x=94−231
Solution
x1=94−231,x2=94+231
Alternative Form
x1≈−0.792837,x2≈1.681725
Show Solution
