Answer:
c = 1 ± √577 / 16
Step-by-step explanation:
Step 1: Move your term to the left side
c = 8c^2 - 18
c - (8c^2 - 18) = 0
Step 2: Distribute
c - (8c^2 - 18) 0
c - 8c^2 + 18 = 0
Step 3: Rearrange terms
c - 8c^2 + 18 = 0
-8c^2 + c + 18 = 0
Step 4 : Common factor
-8c^2 + c + 18 = 0
- (8c^2 - c - 18) = 0
Step 5: Divide both sides of the equation by the same term
- (8c^2 - c - 18 ) = 0
8c^2 - c - 18 =0
Step 6: Use the quadratic formula
= − ± √b^2 - 4ac / 2a
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
8c^2 - c - 18 = 0
a = 8
b = -1
c = -18
c = -(-1) ± √(-1)^2 - 4 * 8(-18) / 2 * 8
Step 7: Simplify
Evaluate the exponent: c = 1 ± √(-1)^2 - 4 * 8(-18) / 2 * 8
c = 1 ± √1 - 4 * 8(-18) / 2 * 8
Multiply the number: c = 1 ± √1 -4 * 8(-18) / 2 * 8
c = 1 ± √1 + 576 / 2 * 8
Add the numbers: c = 1 ± √1 + 576 / 2 * 8
c = 1 ± √577 / 2* 8
Multiply the numbers: c = 1 ± √577 / 2 * 8
c = 1 ± √577 / 16
Step 8: Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
c = 1 + √577 / 16
c = 1 - √577 / 16
Step 9: Solve
Rearrange and isolate the variable to find each solution
c = 1 ± √577 / 16
Solution:
c = 1 ± √577 / 16
