What are the solutions to the equation c=(2x-3)(2x-2)-2x(x-5) ?

The solutions to the equation c=(2x-3)(2x-2)-2x(x-5) are x=sqrt((c-6)/2),x=-sqrt((c-6)/2)

Find the zeros of c=(2x-3)(2x-2)-2x(x-5)

The zeros of c=(2x-3)(2x-2)-2x(x-5) are x=sqrt((c-6)/2),x=-sqrt((c-6)/2)

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c = (2 x - 3) (2 x - 2) - 2 x (x - 5)

x = \frac{c - 6}{2}, x = - \frac{c - 6}{2}

Solution steps

c = (2 x - 3) (2 x - 2) - 2 x (x - 5)

Expand

(2 x - 3) (2 x - 2) - 2 x (x - 5) : 2 x^{2} + 6

c = 2 x^{2} + 6

Switch sides

2 x^{2} + 6 = c

Move

c

to the left side

2 x^{2} + 6 - c = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 0 \pm 0 ^{2} - 4 \cdot 2 ( 6 - c )}{2 \cdot 2}

Simplify

0^{2} - 4 \cdot 2 (6 - c) : 22 c - 6

x_{1, 2} = \frac{- 0 \pm 2 2 c - 6}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 0 + 2 2 c - 6}{2 \cdot 2}, x_{2} = \frac{- 0 - 2 2 c - 6}{2 \cdot 2}

x = \frac{- 0 + 2 2 c - 6}{2 \cdot 2} : \frac{c - 6}{2}

x = \frac{- 0 - 2 2 c - 6}{2 \cdot 2} : - \frac{c - 6}{2}

The solutions to the quadratic equation are:

x = \frac{c - 6}{2}, x = - \frac{c - 6}{2}

x^{2} - x - a = 0

(x + 1)^{2} = 4 x

- 6 x^{2} + 5 x - 1 = 0

64 r^{2} + 1 = 26

(3 x - 2)^{2} = 7

What are the solutions to the equation c=(2x-3)(2x-2)-2x(x-5) ?
The solutions to the equation c=(2x-3)(2x-2)-2x(x-5) are x=sqrt((c-6)/2),x=-sqrt((c-6)/2)
Find the zeros of c=(2x-3)(2x-2)-2x(x-5)
The zeros of c=(2x-3)(2x-2)-2x(x-5) are x=sqrt((c-6)/2),x=-sqrt((c-6)/2)