Solve by Completing the Square -4x^2-11x=7

Problem

−4*x2−11*x=7

Solution

1. Divide both sides by the leading coefficient −4 to make the x2 coefficient equal to 1

x2+11/4*x=−7/4

2. Identify the coefficient of x which is 11/4 and calculate the value needed to complete the square by taking half of it and squaring the result.

1/2⋅11/4=11/8

(11/8)2=121/64

3. Add 121/64 to both sides of the equation to maintain equality.

x2+11/4*x+121/64=−7/4+121/64

4. Simplify the right side by finding a common denominator.

−7/4=−112/64

−112/64+121/64=9/64

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

(x+11/8)2=9/64

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

x+11/8=±√(,9/64)

x+11/8=±3/8

7. Solve for x by subtracting 11/8 from both sides.

x=−11/8±3/8

8. Calculate the two distinct solutions.

x=−11/8+3/8=−8/8=−1

x=−11/8−3/8=−14/8=−7/4

Final Answer

x=−1,−7/4

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