# Solve for y square root of -25y+19=y-7 -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
Simplify each side of the equation.
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
Solve for y.
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

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