Algebra
Calculus
Trigonometry
Matrix
Question
Find the roots
x1=−7−14+739,x2=7−14+739
Alternative Form
x1≈−0.778735,x2≈0.778735
Evaluate
7x4−5+4x2
To find the roots of the expression,set the expression equal to 0
7x4−5+4x2=0
Solve the equation using substitution t=x2
7t2−5+4t=0
Rewrite in standard form
7t2+4t−5=0
Substitute a=7,b=4 and c=−5 into the quadratic formula t=2a−b±b2−4ac
t=2×7−4±42−4×7(−5)
Simplify the expression
t=14−4±42−4×7(−5)
Simplify the expression
More Steps
Evaluate
42−4×7(−5)
Multiply
More Steps
Multiply the terms
4×7(−5)
Rewrite the expression
−4×7×5
Multiply the terms
−140
42−(−140)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
42+140
Evaluate the power
16+140
Add the numbers
156
t=14−4±156
Simplify the radical expression
More Steps
Evaluate
156
Write the expression as a product where the root of one of the factors can be evaluated
4×39
Write the number in exponential form with the base of 2
22×39
The root of a product is equal to the product of the roots of each factor
22×39
Reduce the index of the radical and exponent with 2
239
t=14−4±239
Separate the equation into 2 possible cases
t=14−4+239t=14−4−239
Simplify the expression
More Steps
Evaluate
t=14−4+239
Divide the terms
More Steps
Evaluate
14−4+239
Rewrite the expression
142(−2+39)
Cancel out the common factor 2
7−2+39
t=7−2+39
t=7−2+39t=14−4−239
Simplify the expression
More Steps
Evaluate
t=14−4−239
Divide the terms
More Steps
Evaluate
14−4−239
Rewrite the expression
142(−2−39)
Cancel out the common factor 2
7−2−39
Use b−a=−ba=−ba to rewrite the fraction
−72+39
t=−72+39
t=7−2+39t=−72+39
Substitute back
x2=7−2+39x2=−72+39
Solve the equation for x
More Steps
Substitute back
x2=7−2+39
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±7−2+39
Simplify the expression
More Steps
Evaluate
7−2+39
To take a root of a fraction,take the root of the numerator and denominator separately
7−2+39
Multiply by the Conjugate
7×7−2+39×7
Multiply the numbers
7×7−14+739
When a square root of an expression is multiplied by itself,the result is that expression
7−14+739
x=±7−14+739
Separate the equation into 2 possible cases
x=7−14+739x=−7−14+739
x=7−14+739x=−7−14+739x2=−72+39
Solve the equation for x
More Steps
Substitute back
x2=−72+39
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±−72+39
Simplify the expression
More Steps
Evaluate
−72+39
Evaluate the power
72+39×−1
Evaluate the power
72+39×i
Evaluate the power
714+739i
x=±714+739i
Separate the equation into 2 possible cases
x=714+739ix=−714+739i
x=7−14+739x=−7−14+739x=714+739ix=−714+739i
Calculate
x=7−14+739x=−7−14+739
Solution
x1=−7−14+739,x2=7−14+739
Alternative Form
x1≈−0.778735,x2≈0.778735
Show Solution
