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In the following exercises, solve by completing the square-

x2+5x=2

Short Answer

Expert verified

The solution is33-52,-33-52

Step by step solution

01

Step 1. Given information

The equation:x2+5x=2

02

Step 2. Calculation

Solving the equation,

x2+5x=2

⇒x2+5x+12×52=2+12×52

⇒x2+5x+254=2+254⇒4x2+20x+254=8+254⇒4x2+20x+25=33

⇒4x2+10x+10x+25=33

⇒2x(2x+5)+5(2x+5)=33

⇒(2x+5)2=33

⇒2x+5=±33

localid="1645264846365" ⇒x=±33-52⇒x=33-52,-33-52

The required value of xis,

33-52,-33-52

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