Question
Solve the equation(The real numbers system)
x∈/R
Alternative Form
No real solution
Evaluate
5×8x2−7(12x−3)=−35
Multiply the numbers
40x2−7(12x−3)=−35
Expand the expression
More Steps

Evaluate
−7(12x−3)
Apply the distributive property
−7×12x−(−7×3)
Multiply the numbers
−84x−(−7×3)
Multiply the numbers
−84x−(−21)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−84x+21
40x2−84x+21=−35
Move the expression to the left side
40x2−84x+56=0
Substitute a=40,b=−84 and c=56 into the quadratic formula x=2a−b±b2−4ac
x=2×4084±(−84)2−4×40×56
Simplify the expression
x=8084±(−84)2−4×40×56
Simplify the expression
More Steps

Evaluate
(−84)2−4×40×56
Multiply the terms
More Steps

Multiply the terms
4×40×56
Multiply the terms
160×56
Multiply the numbers
8960
(−84)2−8960
Rewrite the expression
842−8960
Evaluate the power
7056−8960
Subtract the numbers
−1904
x=8084±−1904
Solution
x∈/R
Alternative Form
No real solution
Show Solution

Solve the equation(The complex numbers system)
Solve using the quadratic formula in the complex numbers system
Solve by completing the square in the complex numbers system
Solve using the PQ formula in the complex numbers system
x1=2021−20119i,x2=2021+20119i
Alternative Form
x1≈1.05−0.545436i,x2≈1.05+0.545436i
Evaluate
5×8x2−7(12x−3)=−35
Multiply the numbers
40x2−7(12x−3)=−35
Expand the expression
More Steps

Evaluate
−7(12x−3)
Apply the distributive property
−7×12x−(−7×3)
Multiply the numbers
−84x−(−7×3)
Multiply the numbers
−84x−(−21)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−84x+21
40x2−84x+21=−35
Move the expression to the left side
40x2−84x+56=0
Substitute a=40,b=−84 and c=56 into the quadratic formula x=2a−b±b2−4ac
x=2×4084±(−84)2−4×40×56
Simplify the expression
x=8084±(−84)2−4×40×56
Simplify the expression
More Steps

Evaluate
(−84)2−4×40×56
Multiply the terms
More Steps

Multiply the terms
4×40×56
Multiply the terms
160×56
Multiply the numbers
8960
(−84)2−8960
Rewrite the expression
842−8960
Evaluate the power
7056−8960
Subtract the numbers
−1904
x=8084±−1904
Simplify the radical expression
More Steps

Evaluate
−1904
Evaluate the power
1904×−1
Evaluate the power
1904×i
Evaluate the power
More Steps

Evaluate
1904
Write the expression as a product where the root of one of the factors can be evaluated
16×119
Write the number in exponential form with the base of 4
42×119
The root of a product is equal to the product of the roots of each factor
42×119
Reduce the index of the radical and exponent with 2
4119
4119×i
x=8084±4119×i
Separate the equation into 2 possible cases
x=8084+4119×ix=8084−4119×i
Simplify the expression
More Steps

Evaluate
x=8084+4119×i
Divide the terms
More Steps

Evaluate
8084+4119×i
Rewrite the expression
804(21+119×i)
Cancel out the common factor 4
2021+119×i
Simplify
2021+20119i
x=2021+20119i
x=2021+20119ix=8084−4119×i
Simplify the expression
More Steps

Evaluate
x=8084−4119×i
Divide the terms
More Steps

Evaluate
8084−4119×i
Rewrite the expression
804(21−119×i)
Cancel out the common factor 4
2021−119×i
Simplify
2021−20119i
x=2021−20119i
x=2021+20119ix=2021−20119i
Solution
x1=2021−20119i,x2=2021+20119i
Alternative Form
x1≈1.05−0.545436i,x2≈1.05+0.545436i
Show Solution
