Algebra
Calculus
Trigonometry
Matrix
Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
r1=21−33,r2=21+33
Alternative Form
r1≈−2.372281,r2≈3.372281
Evaluate
r2−r−8=0
Substitute a=1,b=−1 and c=−8 into the quadratic formula r=2a−b±b2−4ac
r=21±(−1)2−4(−8)
Simplify the expression
More Steps
Evaluate
(−1)2−4(−8)
Evaluate the power
1−4(−8)
Multiply the numbers
More Steps
Evaluate
4(−8)
Multiplying or dividing an odd number of negative terms equals a negative
−4×8
Multiply the numbers
−32
1−(−32)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+32
Add the numbers
33
r=21±33
Separate the equation into 2 possible cases
r=21+33r=21−33
Solution
r1=21−33,r2=21+33
Alternative Form
r1≈−2.372281,r2≈3.372281
Show Solution
Rewrite the equation
17x2+17y2=x4+y4+64+2x2y2
Evaluate
r2−r−8=0
Rewrite the expression
r2−r=8
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
x2+y2−r=8
Simplify the expression
−r=−x2−y2+8
Square both sides of the equation
(−r)2=(−x2−y2+8)2
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
x2+y2=(−x2−y2+8)2
Calculate
x2+y2=x4+y4+64+2x2y2−16x2−16y2
Move the expression to the left side
x2+y2−(−16x2−16y2)=x4+y4+64+2x2y2
Calculate
More Steps
Evaluate
x2+16x2
Collect like terms by calculating the sum or difference of their coefficients
(1+16)x2
Add the numbers
17x2
17x2+y2=x4+y4+64+2x2y2−16y2
Solution
More Steps
Evaluate
y2+16y2
Collect like terms by calculating the sum or difference of their coefficients
(1+16)y2
Add the numbers
17y2
17x2+17y2=x4+y4+64+2x2y2
Show Solution
Graph
