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Popular >

solvefor a,p(a-4)=(a-4)^2-5

Solution

solve for

a, p (a - 4) = (a - 4)^{2} - 5

Solution

a = \frac{8 + p + p ^{2} + 20}{2}, a = \frac{8 + p - p ^{2} + 20}{2}

Solution steps

p (a - 4) = (a - 4)^{2} - 5

Expand

p (a - 4) : a p - 4 p

Expand

(a - 4)^{2} - 5 : a^{2} - 8 a + 11

a p - 4 p = a^{2} - 8 a + 11

Switch sides

a^{2} - 8 a + 11 = a p - 4 p

Move

4 p

to the left side

a^{2} - 8 a + 11 + 4 p = a p

Move

a p

to the left side

a^{2} - 8 a + 11 + 4 p - a p = 0

Write in the standard form

a x^{2} + b x + c = 0

a^{2} - (8 + p) a + 11 + 4 p = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- ( - 8 - p ) \pm ( - 8 - p ) ^{2} - 4 \cdot 1 \cdot ( 11 + 4 p )}{2 \cdot 1}

Simplify

(- 8 - p)^{2} - 4 \cdot 1 \cdot (11 + 4 p) : p^{2} + 20

a_{1, 2} = \frac{- ( - 8 - p ) \pm p ^{2} + 20}{2 \cdot 1}

Separate the solutions

a_{1} = \frac{- ( - 8 - p ) + p ^{2} + 20}{2 \cdot 1}, a_{2} = \frac{- ( - 8 - p ) - p ^{2} + 20}{2 \cdot 1}

a = \frac{- ( - 8 - p ) + p ^{2} + 20}{2 \cdot 1} : \frac{8 + p + p ^{2} + 20}{2}

a = \frac{- ( - 8 - p ) - p ^{2} + 20}{2 \cdot 1} : \frac{8 + p - p ^{2} + 20}{2}

The solutions to the quadratic equation are:

a = \frac{8 + p + p ^{2} + 20}{2}, a = \frac{8 + p - p ^{2} + 20}{2}

Popular Examples

solvefor x,x^2+8x+1=0 solve for

x, x^{2} + 8 x + 1 = 0

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(x + 3)^{2} - 2 = 0

3 x^{2} + 60 = 36 x