Solve -24/49{left(x+1/4right)}^2+3/2

$$- \frac{ 24 }{ 49 } { \left(x+ \frac{ 1 }{ 4 } \right) }^{ 2 } + \frac{ 3 }{ 2 }$$

Evaluate

$$\frac{72-12x-24x^{2}}{49}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{1}{4}\right)^{2}.

$$-\frac{24}{49}\left(x^{2}+\frac{1}{2}x+\frac{1}{16}\right)+\frac{3}{2}$$

Use the distributive property to multiply -\frac{24}{49} by x^{2}+\frac{1}{2}x+\frac{1}{16}.

$$-\frac{24}{49}x^{2}-\frac{12}{49}x-\frac{3}{98}+\frac{3}{2}$$

Add -\frac{3}{98} and \frac{3}{2} to get \frac{72}{49}.

$$-\frac{24}{49}x^{2}-\frac{12}{49}x+\frac{72}{49}$$

Expand

$$\frac{72-12x-24x^{2}}{49}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{1}{4}\right)^{2}.

$$-\frac{24}{49}\left(x^{2}+\frac{1}{2}x+\frac{1}{16}\right)+\frac{3}{2}$$

Use the distributive property to multiply -\frac{24}{49} by x^{2}+\frac{1}{2}x+\frac{1}{16}.

$$-\frac{24}{49}x^{2}-\frac{12}{49}x-\frac{3}{98}+\frac{3}{2}$$

Add -\frac{3}{98} and \frac{3}{2} to get \frac{72}{49}.

$$-\frac{24}{49}x^{2}-\frac{12}{49}x+\frac{72}{49}$$