Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(b1,c1)=(101+21,−70+7021)(b2,c2)=(101−21,−70−7021)
Evaluate
{bc=700b−c700b−c=140
Solve the equation for c
More Steps
Evaluate
700b−c=140
Move the expression to the right-hand side and change its sign
−c=140−700b
Change the signs on both sides of the equation
c=−140+700b
{bc=700b−cc=−140+700b
Substitute the given value of c into the equation bc=700b−c
b(−140+700b)=700b−(−140+700b)
Simplify
More Steps
Evaluate
700b−(−140+700b)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
700b+140−700b
The sum of two opposites equals 0
More Steps
Evaluate
700b−700b
Collect like terms
(700−700)b
Add the coefficients
0×b
Calculate
0
0+140
Remove 0
140
b(−140+700b)=140
Expand the expression
More Steps
Evaluate
b(−140+700b)
Apply the distributive property
b(−140)+b×700b
Use the commutative property to reorder the terms
−140b+b×700b
Multiply the terms
More Steps
Evaluate
b×700b
Use the commutative property to reorder the terms
700b×b
Multiply the terms
700b2
−140b+700b2
−140b+700b2=140
Move the expression to the left side
−140b+700b2−140=0
Rewrite in standard form
700b2−140b−140=0
Substitute a=700,b=−140 and c=−140 into the quadratic formula b=2a−b±b2−4ac
b=2×700140±(−140)2−4×700(−140)
Simplify the expression
b=1400140±(−140)2−4×700(−140)
Simplify the expression
More Steps
Evaluate
(−140)2−4×700(−140)
Multiply
More Steps
Multiply the terms
4×700(−140)
Rewrite the expression
−4×700×140
Multiply the terms
−392000
(−140)2−(−392000)
Rewrite the expression
1402−(−392000)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1402+392000
Evaluate the power
19600+392000
Add the numbers
411600
b=1400140±411600
Simplify the radical expression
More Steps
Evaluate
411600
Write the expression as a product where the root of one of the factors can be evaluated
19600×21
Write the number in exponential form with the base of 140
1402×21
The root of a product is equal to the product of the roots of each factor
1402×21
Reduce the index of the radical and exponent with 2
14021
b=1400140±14021
Separate the equation into 2 possible cases
b=1400140+14021b=1400140−14021
Simplify the expression
More Steps
Evaluate
b=1400140+14021
Divide the terms
More Steps
Evaluate
1400140+14021
Rewrite the expression
1400140(1+21)
Cancel out the common factor 140
101+21
b=101+21
b=101+21b=1400140−14021
Simplify the expression
More Steps
Evaluate
b=1400140−14021
Divide the terms
More Steps
Evaluate
1400140−14021
Rewrite the expression
1400140(1−21)
Cancel out the common factor 140
101−21
b=101−21
b=101+21b=101−21
Evaluate the logic
b=101+21∪b=101−21
Rearrange the terms
{b=101+21c=−140+700b∪{b=101−21c=−140+700b
Calculate
More Steps
Evaluate
{b=101+21c=−140+700b
Substitute the given value of b into the equation c=−140+700b
c=−140+700×101+21
Calculate
c=−70+7021
Calculate
{b=101+21c=−70+7021
{b=101+21c=−70+7021∪{b=101−21c=−140+700b
Calculate
More Steps
Evaluate
{b=101−21c=−140+700b
Substitute the given value of b into the equation c=−140+700b
c=−140+700×101−21
Calculate
c=−70−7021
Calculate
{b=101−21c=−70−7021
{b=101+21c=−70+7021∪{b=101−21c=−70−7021
Check the solution
More Steps
Check the solution
⎩⎨⎧101+21×(−70+7021)=700×101+21−(−70+7021)700×101+21−(−70+7021)=140
Simplify
{140=140140=140
Evaluate
true
{b=101+21c=−70+7021∪{b=101−21c=−70−7021
Check the solution
More Steps
Check the solution
⎩⎨⎧101−21×(−70−7021)=700×101−21−(−70−7021)700×101−21−(−70−7021)=140
Simplify
{140=140140=140
Evaluate
true
{b=101+21c=−70+7021∪{b=101−21c=−70−7021
Solution
(b1,c1)=(101+21,−70+7021)(b2,c2)=(101−21,−70−7021)
Show Solution
