Last question. 50 points!​

The equation has two solutions which are 2 and -1.5.

Step-by-step explanation:

Step 1 :- Move constant to the left-hand side and change their sign.

Step 2 :- Subtract 2 from 7.

Step 3 :- Square root on both side of expression.

➻ 2w² - 19w + 31 = 25 - 20w + 4w²

Step 3 :- Move expression to the left-hand side and change their sign.

➻ 2w² - 19w + 31 - 25 + 20w - 4w² = 0

Step 4 :- Combine like terms.

➻ -2w² + w + 6 = 0

Step 5 :- Change the sign on both side of equation.

➻ 2w² - w - 6 = 0

Step 6 :- Split the term -w as 3w - 4w.

➻ 2w² + 3w - 4w - 6 = 0

Step 7 :- Factor out w from the first pair and -2 from the second pair.

➻ w ( 2w + 3 ) - 2( 2w + 3 ) = 0

Step 8 :- Factor out w + 3 from the expression.

➻ ( 2w + 3 ) ( w - 2 ) = 0

Step 9 :- Using the zero product property.

➻ 2w + 3 = 0, w - 2 = 0

Step 10 :- Solve for w.

w = = 1.5 , and w = 2

Thus, This equation has two solutions.

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