Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1=221−501,x2=221−381,x3=221+381,x4=221+501
Alternative Form
x1≈−0.691515,x2≈0.740389,x3≈20.259611,x4≈21.691515
Evaluate
152=(21−x)2x2
Use the commutative property to reorder the terms
152=x2(21−x)2
Swap the sides of the equation
x2(21−x)2=152
Expand the expression
More Steps
Evaluate
x2(21−x)2
Expand the expression
More Steps
Evaluate
(21−x)2
Use (a−b)2=a2−2ab+b2 to expand the expression
212−2×21x+x2
Calculate
441−42x+x2
x2(441−42x+x2)
Apply the distributive property
x2×441−x2×42x+x2×x2
Use the commutative property to reorder the terms
441x2−x2×42x+x2×x2
Multiply the terms
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Evaluate
x2×42x
Use the commutative property to reorder the terms
42x2×x
Multiply the terms
42x3
441x2−42x3+x2×x2
Multiply the terms
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Evaluate
x2×x2
Use the product rule an×am=an+m to simplify the expression
x2+2
Add the numbers
x4
441x2−42x3+x4
441x2−42x3+x4=152
Expand the expression
441x2−42x3+x4=225
Move the expression to the left side
441x2−42x3+x4−225=0
Factor the expression
(21x−x2+15)(21x−x2−15)=0
Separate the equation into 2 possible cases
21x−x2+15=021x−x2−15=0
Solve the equation
More Steps
Evaluate
21x−x2+15=0
Rewrite in standard form
−x2+21x+15=0
Multiply both sides
x2−21x−15=0
Substitute a=1,b=−21 and c=−15 into the quadratic formula x=2a−b±b2−4ac
x=221±(−21)2−4(−15)
Simplify the expression
More Steps
Evaluate
(−21)2−4(−15)
Multiply the numbers
(−21)2−(−60)
Rewrite the expression
212−(−60)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
212+60
Evaluate the power
441+60
Add the numbers
501
x=221±501
Separate the equation into 2 possible cases
x=221+501x=221−501
x=221+501x=221−50121x−x2−15=0
Solve the equation
More Steps
Evaluate
21x−x2−15=0
Rewrite in standard form
−x2+21x−15=0
Multiply both sides
x2−21x+15=0
Substitute a=1,b=−21 and c=15 into the quadratic formula x=2a−b±b2−4ac
x=221±(−21)2−4×15
Simplify the expression
More Steps
Evaluate
(−21)2−4×15
Multiply the numbers
(−21)2−60
Rewrite the expression
212−60
Evaluate the power
441−60
Subtract the numbers
381
x=221±381
Separate the equation into 2 possible cases
x=221+381x=221−381
x=221+501x=221−501x=221+381x=221−381
Solution
x1=221−501,x2=221−381,x3=221+381,x4=221+501
Alternative Form
x1≈−0.691515,x2≈0.740389,x3≈20.259611,x4≈21.691515
Show Solution
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