# Solve for c 5.29=4.41+c^2-2*2.1ccos(71)

5.29=4.41+c2-2⋅2.1 ccos (71)
Rewrite the equation as 4.41+c2-2⋅(2.1ccos(71))=5.29.
4.41+c2-2⋅(2.1ccos(71))=5.29
Simplify each term.
Evaluate cos(71).
4.41+c2-2⋅(2.1c⋅0.32556815)=5.29
Multiply 0.32556815 by 2.1.
4.41+c2-2⋅(0.68369312c)=5.29
Multiply 0.68369312 by -2.
4.41+c2-1.36738624c=5.29
4.41+c2-1.36738624c=5.29
Move all terms to the left side of the equation and simplify.
Move 5.29 to the left side of the equation by subtracting it from both sides.
4.41+c2-1.36738624c-5.29=0
Subtract 5.29 from 4.41.
c2-1.36738624c-0.88=0
c2-1.36738624c-0.88=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-1.36738624, and c=-0.88 into the quadratic formula and solve for c.
1.36738624±(-1.36738624)2-4⋅(1⋅-0.88)2⋅1
Simplify.
Simplify the numerator.
Raise -1.36738624 to the power of 2.
c=1.36738624±1.86974515-4⋅(1⋅-0.88)2⋅1
Multiply -0.88 by 1.
c=1.36738624±1.86974515-4⋅-0.882⋅1
Multiply -4 by -0.88.
c=1.36738624±1.86974515+3.522⋅1
c=1.36738624±5.389745152⋅1
c=1.36738624±5.389745152⋅1
Multiply 2 by 1.
c=1.36738624±5.389745152
c=1.36738624±5.389745152
The result can be shown in multiple forms.
Exact Form:
c=1.36738624±5.389745152
Decimal Form:
c=1.84448435…,-0.47709810…
Solve for c 5.29=4.41+c^2-2*2.1ccos(71)

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