Evaluate the expression when c=8.
c² - 18​

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

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