Solve 4/4[(2x-x+3/2)^2+12x-11x^2/16]=

$$\frac { 4 } { 4 } [ ( 2 x - \frac { x + 3 } { 2 } ) ^ { 2 } + \frac { 12 x - 11 x ^ { 2 } } { 16 } ] =$$

Evaluate

$$\frac{\left(5x-6\right)^{2}}{16}$$

Short Solution Steps

Divide 4 by 4 to get 1.

$$1\left(\left(2x-\frac{x+3}{2}\right)^{2}+\frac{12x-11x^{2}}{16}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{2}{2}.

$$1\left(\left(\frac{2\times 2x}{2}-\frac{x+3}{2}\right)^{2}+\frac{12x-11x^{2}}{16}\right)$$

Since \frac{2\times 2x}{2} and \frac{x+3}{2} have the same denominator, subtract them by subtracting their numerators.

$$1\left(\left(\frac{2\times 2x-\left(x+3\right)}{2}\right)^{2}+\frac{12x-11x^{2}}{16}\right)$$

Do the multiplications in 2\times 2x-\left(x+3\right).

$$1\left(\left(\frac{4x-x-3}{2}\right)^{2}+\frac{12x-11x^{2}}{16}\right)$$

Combine like terms in 4x-x-3.

$$1\left(\left(\frac{3x-3}{2}\right)^{2}+\frac{12x-11x^{2}}{16}\right)$$

To raise \frac{3x-3}{2} to a power, raise both numerator and denominator to the power and then divide.

$$1\left(\frac{\left(3x-3\right)^{2}}{2^{2}}+\frac{12x-11x^{2}}{16}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2^{2} and 16 is 16. Multiply \frac{\left(3x-3\right)^{2}}{2^{2}} times \frac{4}{4}.

$$1\left(\frac{4\left(3x-3\right)^{2}}{16}+\frac{12x-11x^{2}}{16}\right)$$

Since \frac{4\left(3x-3\right)^{2}}{16} and \frac{12x-11x^{2}}{16} have the same denominator, add them by adding their numerators.

$$1\times \frac{4\left(3x-3\right)^{2}+12x-11x^{2}}{16}$$

Do the multiplications in 4\left(3x-3\right)^{2}+12x-11x^{2}.

$$1\times \frac{36x^{2}-72x+36+12x-11x^{2}}{16}$$

Combine like terms in 36x^{2}-72x+36+12x-11x^{2}.

$$1\times \frac{25x^{2}-60x+36}{16}$$

Express 1\times \frac{25x^{2}-60x+36}{16} as a single fraction.

$$\frac{25x^{2}-60x+36}{16}$$

Expand

$$\frac{25x^{2}}{16}-\frac{15x}{4}+\frac{9}{4}$$

Short Solution Steps

Divide 4 by 4 to get 1.

$$1\left(\left(2x-\frac{x+3}{2}\right)^{2}+\frac{12x-11x^{2}}{16}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{2}{2}.

$$1\left(\left(\frac{2\times 2x}{2}-\frac{x+3}{2}\right)^{2}+\frac{12x-11x^{2}}{16}\right)$$

Since \frac{2\times 2x}{2} and \frac{x+3}{2} have the same denominator, subtract them by subtracting their numerators.

$$1\left(\left(\frac{2\times 2x-\left(x+3\right)}{2}\right)^{2}+\frac{12x-11x^{2}}{16}\right)$$

Do the multiplications in 2\times 2x-\left(x+3\right).

$$1\left(\left(\frac{4x-x-3}{2}\right)^{2}+\frac{12x-11x^{2}}{16}\right)$$

Combine like terms in 4x-x-3.

$$1\left(\left(\frac{3x-3}{2}\right)^{2}+\frac{12x-11x^{2}}{16}\right)$$

To raise \frac{3x-3}{2} to a power, raise both numerator and denominator to the power and then divide.

$$1\left(\frac{\left(3x-3\right)^{2}}{2^{2}}+\frac{12x-11x^{2}}{16}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2^{2} and 16 is 16. Multiply \frac{\left(3x-3\right)^{2}}{2^{2}} times \frac{4}{4}.

$$1\left(\frac{4\left(3x-3\right)^{2}}{16}+\frac{12x-11x^{2}}{16}\right)$$

Since \frac{4\left(3x-3\right)^{2}}{16} and \frac{12x-11x^{2}}{16} have the same denominator, add them by adding their numerators.

$$1\times \frac{4\left(3x-3\right)^{2}+12x-11x^{2}}{16}$$

Do the multiplications in 4\left(3x-3\right)^{2}+12x-11x^{2}.

$$1\times \frac{36x^{2}-72x+36+12x-11x^{2}}{16}$$

Combine like terms in 36x^{2}-72x+36+12x-11x^{2}.

$$1\times \frac{25x^{2}-60x+36}{16}$$

Express 1\times \frac{25x^{2}-60x+36}{16} as a single fraction.

$$\frac{25x^{2}-60x+36}{16}$$