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Solve each equation by completing the square.

x2x6=0

Short Answer

Expert verified

The solutions of the quadratic equation are-2 and 3.

Step by step solution

01

Step 1. Complete the square

Complete the square to solve the quadratic equations by isolatingx2 andbx-terms.

x2x6=0x2x6+14=0+14        Since  122=14  add  to  each  sidex2x+146+6=14+6         Add  6  to  each  side x2x+14=254

02

Step 2. Take the square root of each side

First factor x2x+14, then take square root of each side.

x122=254x122=±254x12=±52

03

Step 3. Write the solutions

Add 12to both sides and separate the solutions.

x12+12=12±52x=1252      or     x=12+52x=2    or  x=3

Therefore, the solutions of the equation are -2and 3.

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