Algebra
Calculus
Trigonometry
Matrix
Question
Find the roots
x1=4−23,x2=4+23
Alternative Form
x1≈−0.795832,x2≈8.795832
Evaluate
x2−8x−7
To find the roots of the expression,set the expression equal to 0
x2−8x−7=0
Substitute a=1,b=−8 and c=−7 into the quadratic formula x=2a−b±b2−4ac
x=28±(−8)2−4(−7)
Simplify the expression
More Steps
Evaluate
(−8)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
(−8)2−(−28)
Rewrite the expression
82−(−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
82+28
Evaluate the power
64+28
Add the numbers
92
x=28±92
Simplify the radical expression
More Steps
Evaluate
92
Write the expression as a product where the root of one of the factors can be evaluated
4×23
Write the number in exponential form with the base of 2
22×23
The root of a product is equal to the product of the roots of each factor
22×23
Reduce the index of the radical and exponent with 2
223
x=28±223
Separate the equation into 2 possible cases
x=28+223x=28−223
Simplify the expression
More Steps
Evaluate
x=28+223
Divide the terms
More Steps
Evaluate
28+223
Rewrite the expression
22(4+23)
Reduce the fraction
4+23
x=4+23
x=4+23x=28−223
Simplify the expression
More Steps
Evaluate
x=28−223
Divide the terms
More Steps
Evaluate
28−223
Rewrite the expression
22(4−23)
Reduce the fraction
4−23
x=4−23
x=4+23x=4−23
Solution
x1=4−23,x2=4+23
Alternative Form
x1≈−0.795832,x2≈8.795832
Show Solution
