Algebra
Calculus
Trigonometry
Matrix
Question
Find the roots
x1=1−22,x2=1+22
Alternative Form
x1≈−1.828427,x2≈3.828427
Evaluate
x2−2x−7
To find the roots of the expression,set the expression equal to 0
x2−2x−7=0
Substitute a=1,b=−2 and c=−7 into the quadratic formula x=2a−b±b2−4ac
x=22±(−2)2−4(−7)
Simplify the expression
More Steps
Evaluate
(−2)2−4(−7)
Multiply the numbers
More Steps
Evaluate
4(−7)
Multiplying or dividing an odd number of negative terms equals a negative
−4×7
Multiply the numbers
−28
(−2)2−(−28)
Rewrite the expression
22−(−28)
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+28
Evaluate the power
4+28
Add the numbers
32
x=22±32
Simplify the radical expression
More Steps
Evaluate
32
Write the expression as a product where the root of one of the factors can be evaluated
16×2
Write the number in exponential form with the base of 4
42×2
The root of a product is equal to the product of the roots of each factor
42×2
Reduce the index of the radical and exponent with 2
42
x=22±42
Separate the equation into 2 possible cases
x=22+42x=22−42
Simplify the expression
More Steps
Evaluate
x=22+42
Divide the terms
More Steps
Evaluate
22+42
Rewrite the expression
22(1+22)
Reduce the fraction
1+22
x=1+22
x=1+22x=22−42
Simplify the expression
More Steps
Evaluate
x=22−42
Divide the terms
More Steps
Evaluate
22−42
Rewrite the expression
22(1−22)
Reduce the fraction
1−22
x=1−22
x=1+22x=1−22
Solution
x1=1−22,x2=1+22
Alternative Form
x1≈−1.828427,x2≈3.828427
Show Solution
