Solve by Completing the Square x^2-3x-88=0

Problem

x2−3*x−88=0

Solution

1. Move the constant term to the right side of the equation by adding 88 to both sides.

x2−3*x=88

2. Find the value to complete the square by taking half of the coefficient of x which is −3/2 and squaring it.

(−3/2)2=9/4

3. Add the value to both sides of the equation to maintain equality.

x2−3*x+9/4=88+9/4

4. Factor the left side as a perfect square trinomial and simplify the right side using a common denominator.

(x−3/2)2=352/4+9/4

(x−3/2)2=361/4

5. Take the square root of both sides, remembering to include both the positive and negative roots.

x−3/2=±√(,361/4)

x−3/2=±19/2

6. Solve for x by adding 3/2 to both sides and calculating the two possible values.

x=3/2±19/2

x=(3+19)/2⇒x=11

x=(3−19)/2⇒x=−8

Final Answer

x=11,−8

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