What are the solutions to the equation a=(x-6)(x-20)-(x-3)2+50 ?

The solutions to the equation a=(x-6)(x-20)-(x-3)2+50 are x=14+sqrt(a+20),x=14-sqrt(a+20)

Find the zeros of a=(x-6)(x-20)-(x-3)2+50

The zeros of a=(x-6)(x-20)-(x-3)2+50 are x=14+sqrt(a+20),x=14-sqrt(a+20)

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a = (x - 6) (x - 20) - (x - 3) 2 + 50

x = 14 + a + 20, x = 14 - a + 20

Solution steps

a = (x - 6) (x - 20) - (x - 3) \cdot 2 + 50

Expand

(x - 6) (x - 20) - (x - 3) \cdot 2 + 50 : x^{2} - 28 x + 176

a = x^{2} - 28 x + 176

Switch sides

x^{2} - 28 x + 176 = a

Move

a

to the left side

x^{2} - 28 x + 176 - a = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 28 ) \pm ( - 28 ) ^{2} - 4 \cdot 1 \cdot ( 176 - a )}{2 \cdot 1}

Simplify

(- 28)^{2} - 4 \cdot 1 \cdot (176 - a) : 2 a + 20

x_{1, 2} = \frac{- ( - 28 ) \pm 2 a + 20}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 28 ) + 2 a + 20}{2 \cdot 1}, x_{2} = \frac{- ( - 28 ) - 2 a + 20}{2 \cdot 1}

x = \frac{- ( - 28 ) + 2 a + 20}{2 \cdot 1} : 14 + a + 20

x = \frac{- ( - 28 ) - 2 a + 20}{2 \cdot 1} : 14 - a + 20

The solutions to the quadratic equation are:

x = 14 + a + 20, x = 14 - a + 20

(π t - 4)^{2} = 4.1 t - 3

- 6 x = - 9 x^{2} + 8

k^{2} + 10 k + 16 = 0

18 x^{2} - 7 x = 1

y^{2} - 4 y = 5

What are the solutions to the equation a=(x-6)(x-20)-(x-3)2+50 ?
The solutions to the equation a=(x-6)(x-20)-(x-3)2+50 are x=14+sqrt(a+20),x=14-sqrt(a+20)
Find the zeros of a=(x-6)(x-20)-(x-3)2+50
The zeros of a=(x-6)(x-20)-(x-3)2+50 are x=14+sqrt(a+20),x=14-sqrt(a+20)