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Chapter 8: Q23. (page 492)

Solve each equation. Check your solutions.

x2-5x=14

Short Answer

Expert verified

The solution ofx2鈭�5x=14 is role="math" localid="1647953707701" x=7,鈭�2.

Step by step solution

01

Step 1. Subtract.

Subtract from both sides of the given equation.

x2鈭�5x鈭�14=14鈭�14=0

02

Step 2. Factor by using GCF.

Factor by using GCF to get the form xy=0.

x鈭�7x+2=0

03

Step 3. Write zero product property.

For any real numbers x and y, if xy=0 then x=0,y=0 or both x and y equal to zero.

04

Step 4. Apply zero product property.

Apply zero product property to the given equation, x鈭�7x+2=0.

localid="1647954254435" x鈭�7=0orx+2=0x=7x=鈭�2

Therefore, the roots are 7 and -2.

05

Step 5. Check the obtained solution.

To check whether the obtained solution is correct or not, substitute 7 forxand-2forxin the given equation and simplify.

role="math" localid="1647954142827" 72鈭�57=?1449鈭�35=?1414=14LHS=RHS

鈭�22鈭�5鈭�2=?144+10=?1414=14LHS=RHS

Therefore, the obtained solution is correct.

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