-25y+19=y-7

To remove the radical on the left side of the equation, square both sides of the equation.

-25y+192=(y-7)2

Multiply the exponents in ((-25y+19)12)2.

Apply the power rule and multiply exponents, (am)n=amn.

(-25y+19)12⋅2=(y-7)2

Cancel the common factor of 2.

Cancel the common factor.

(-25y+19)12⋅2=(y-7)2

Rewrite the expression.

(-25y+19)1=(y-7)2

(-25y+19)1=(y-7)2

(-25y+19)1=(y-7)2

Simplify.

-25y+19=(y-7)2

-25y+19=(y-7)2

Simplify (y-7)2.

Rewrite (y-7)2 as (y-7)(y-7).

-25y+19=(y-7)(y-7)

Expand (y-7)(y-7) using the FOIL Method.

Apply the distributive property.

-25y+19=y(y-7)-7(y-7)

Apply the distributive property.

-25y+19=y⋅y+y⋅-7-7(y-7)

Apply the distributive property.

-25y+19=y⋅y+y⋅-7-7y-7⋅-7

-25y+19=y⋅y+y⋅-7-7y-7⋅-7

Simplify and combine like terms.

Simplify each term.

Multiply y by y.

-25y+19=y2+y⋅-7-7y-7⋅-7

Move -7 to the left of y.

-25y+19=y2-7⋅y-7y-7⋅-7

Multiply -7 by -7.

-25y+19=y2-7y-7y+49

-25y+19=y2-7y-7y+49

Subtract 7y from -7y.

-25y+19=y2-14y+49

-25y+19=y2-14y+49

-25y+19=y2-14y+49

Since y is on the right side of the equation, switch the sides so it is on the left side of the equation.

y2-14y+49=-25y+19

Move all terms containing y to the left side of the equation.

Add 25y to both sides of the equation.

y2-14y+49+25y=19

Add -14y and 25y.

y2+11y+49=19

y2+11y+49=19

Move 19 to the left side of the equation by subtracting it from both sides.

y2+11y+49-19=0

Subtract 19 from 49.

y2+11y+30=0

Factor y2+11y+30 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 30 and whose sum is 11.

5,6

Write the factored form using these integers.

(y+5)(y+6)=0

(y+5)(y+6)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

y+5=0

y+6=0

Set the first factor equal to 0 and solve.

Set the first factor equal to 0.

y+5=0

Subtract 5 from both sides of the equation.

y=-5

y=-5

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

y+6=0

Subtract 6 from both sides of the equation.

y=-6

y=-6

The final solution is all the values that make (y+5)(y+6)=0 true.

y=-5,-6

y=-5,-6

Exclude the solutions that do not make -25y+19=y-7 true.

No solution

Solve for y square root of -25y+19=y-7