Algebra
Calculus
Trigonometry
Matrix
Question
Find the roots
x1=2−11,x2=2+11
Alternative Form
x1≈−1.316625,x2≈5.316625
Evaluate
x2−4x−7
To find the roots of the expression,set the expression equal to 0
x2−4x−7=0
Substitute a=1,b=−4 and c=−7 into the quadratic formula x=2a−b±b2−4ac
x=24±(−4)2−4(−7)
Simplify the expression
More Steps
Evaluate
(−4)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
(−4)2−(−28)
Rewrite the expression
42−(−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
42+28
Evaluate the power
16+28
Add the numbers
44
x=24±44
Simplify the radical expression
More Steps
Evaluate
44
Write the expression as a product where the root of one of the factors can be evaluated
4×11
Write the number in exponential form with the base of 2
22×11
The root of a product is equal to the product of the roots of each factor
22×11
Reduce the index of the radical and exponent with 2
211
x=24±211
Separate the equation into 2 possible cases
x=24+211x=24−211
Simplify the expression
More Steps
Evaluate
x=24+211
Divide the terms
More Steps
Evaluate
24+211
Rewrite the expression
22(2+11)
Reduce the fraction
2+11
x=2+11
x=2+11x=24−211
Simplify the expression
More Steps
Evaluate
x=24−211
Divide the terms
More Steps
Evaluate
24−211
Rewrite the expression
22(2−11)
Reduce the fraction
2−11
x=2−11
x=2+11x=2−11
Solution
x1=2−11,x2=2+11
Alternative Form
x1≈−1.316625,x2≈5.316625
Show Solution
