Question
Factor the expression
2(x2−11x−29)
Evaluate
2x2−22x−58
Solution
2(x2−11x−29)
Show Solution

Find the roots
x1=211−237,x2=211+237
Alternative Form
x1≈−2.197402,x2≈13.197402
Evaluate
2x2−22x−58
To find the roots of the expression,set the expression equal to 0
2x2−22x−58=0
Substitute a=2,b=−22 and c=−58 into the quadratic formula x=2a−b±b2−4ac
x=2×222±(−22)2−4×2(−58)
Simplify the expression
x=422±(−22)2−4×2(−58)
Simplify the expression
More Steps

Evaluate
(−22)2−4×2(−58)
Multiply
More Steps

Multiply the terms
4×2(−58)
Rewrite the expression
−4×2×58
Multiply the terms
−464
(−22)2−(−464)
Rewrite the expression
222−(−464)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
222+464
Evaluate the power
484+464
Add the numbers
948
x=422±948
Simplify the radical expression
More Steps

Evaluate
948
Write the expression as a product where the root of one of the factors can be evaluated
4×237
Write the number in exponential form with the base of 2
22×237
The root of a product is equal to the product of the roots of each factor
22×237
Reduce the index of the radical and exponent with 2
2237
x=422±2237
Separate the equation into 2 possible cases
x=422+2237x=422−2237
Simplify the expression
More Steps

Evaluate
x=422+2237
Divide the terms
More Steps

Evaluate
422+2237
Rewrite the expression
42(11+237)
Cancel out the common factor 2
211+237
x=211+237
x=211+237x=422−2237
Simplify the expression
More Steps

Evaluate
x=422−2237
Divide the terms
More Steps

Evaluate
422−2237
Rewrite the expression
42(11−237)
Cancel out the common factor 2
211−237
x=211−237
x=211+237x=211−237
Solution
x1=211−237,x2=211+237
Alternative Form
x1≈−2.197402,x2≈13.197402
Show Solution
