Solve by Completing the Square x^2=3/4x-1/8

Problem

x2=3/4*x−1/8

Solution

1. Rearrange the equation into the form x2+b*x=c by subtracting 3/4*x from both sides.

x2−3/4*x=−1/8

2. Identify the coefficient of x which is b=−3/4

3. Calculate the value needed to complete the square by taking half of b and squaring it: (1/2⋅−3/4)2=(−3/8)2=9/64

4. Add 9/64 to both sides of the equation to maintain equality.

x2−3/4*x+9/64=−1/8+9/64

5. Simplify the right side by finding a common denominator: −1/8=−8/64

x2−3/4*x+9/64=1/64

6. Factor the left side as a perfect square trinomial.

(x−3/8)2=1/64

7. Take the square root of both sides, remembering to include the plus-minus sign.

x−3/8=±√(,1/64)

x−3/8=±1/8

8. Solve for x by adding 3/8 to both sides.

x=3/8±1/8

9. Evaluate both possible solutions.

x=3/8+1/8=4/8=1/2

x=3/8−1/8=2/8=1/4

Final Answer

x=1/2,1/4

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