Using the properties of equality, find the solution to the equation 2f5−85+2f=8 .(1 point)
Responses
12
12
166
Start Fraction 16 over 6 End Fraction
8/3
Start Fraction 8 over 3 End Fraction
4
To find the solution to the equation 2f^5 - 85 + 2f = 8, we can follow these steps:
1. Start by isolating the f terms on one side of the equation. Move -85 to the other side by adding 85 to both sides:
2f^5 + 2f = 8 + 85
2f^5 + 2f = 93
2. Rearrange the equation by writing the terms in descending order of their exponents:
2f^5 + 2f - 93 = 0
3. To solve this equation, we can use factoring, the quadratic formula, or other advanced methods. However, since this equation is a fifth-degree polynomial, it doesn't have a simple algebraic solution. Instead, it would require numerical methods or a graphing calculator.
Therefore, the given equation 2f^5 - 85 + 2f = 8 does not have a simple solution that can be found using the properties of equality.
To solve the equation 2f^5 - 8f = 8, we can follow these steps:
Step 1: Move all terms to one side of the equation to set it equal to zero.
2f^5 - 8f - 8 = 0
Step 2: Factor out the common factor.
2(f^5 - 4f - 4) = 0
Step 3: Set each factor equal to zero and solve.
a) f^5 - 4f - 4 = 0
Unfortunately, this equation cannot be solved algebraically using the properties of equality.
To find the solution to the equation 2f^5 - 8^5 + 2f = 8, follow these steps:
Step 1: Combine like terms.
Combine the terms with 'f' on the left side of the equation:
2f^5 + 2f - 8^5 = 8
Step 2: Simplify the exponent.
Evaluate the exponent: 8^5 = 32768.
Therefore, the equation becomes:
2f^5 + 2f - 32768 = 8
Step 3: Isolate the variable.
To isolate 'f', move the constant term to the right side:
2f^5 + 2f = 8 + 32768
Step 4: Combine terms.
Combine the constant terms on the right side:
2f^5 + 2f = 32776
Step 5: Divide by the coefficient of 'f'.
Divide both sides of the equation by 2 to solve for 'f':
(2f^5 + 2f) ÷ 2 = 32776 ÷ 2
f^5 + f = 16388
Step 6: Subtract the constant term.
Subtract 16388 from both sides to isolate 'f':
f^5 + f - 16388 = 0
At this point, you will either need to use a calculator or solve the polynomial equation using numerical methods to find the solutions.