Question
Find the roots
x1=31−31,x2=31+31
Alternative Form
x1≈−1.522588,x2≈2.189255
Evaluate
3x2−2x−10
To find the roots of the expression,set the expression equal to 0
3x2−2x−10=0
Substitute a=3,b=−2 and c=−10 into the quadratic formula x=2a−b±b2−4ac
x=2×32±(−2)2−4×3(−10)
Simplify the expression
x=62±(−2)2−4×3(−10)
Simplify the expression
More Steps

Evaluate
(−2)2−4×3(−10)
Multiply
More Steps

Multiply the terms
4×3(−10)
Any expression multiplied by 1 remains the same
−4×3×10
Multiply the terms
−12×10
Multiply the numbers
−120
(−2)2−(−120)
Rewrite the expression
22−(−120)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22+120
Evaluate the power
4+120
Add the numbers
124
x=62±124
Simplify the radical expression
More Steps

Evaluate
124
Write the expression as a product where the root of one of the factors can be evaluated
4×31
Write the number in exponential form with the base of 2
22×31
The root of a product is equal to the product of the roots of each factor
22×31
Reduce the index of the radical and exponent with 2
231
x=62±231
Separate the equation into 2 possible cases
x=62+231x=62−231
Simplify the expression
More Steps

Evaluate
x=62+231
Divide the terms
More Steps

Evaluate
62+231
Rewrite the expression
62(1+31)
Cancel out the common factor 2
31+31
x=31+31
x=31+31x=62−231
Simplify the expression
More Steps

Evaluate
x=62−231
Divide the terms
More Steps

Evaluate
62−231
Rewrite the expression
62(1−31)
Cancel out the common factor 2
31−31
x=31−31
x=31+31x=31−31
Solution
x1=31−31,x2=31+31
Alternative Form
x1≈−1.522588,x2≈2.189255
Show Solution
