Solve (x-3)^2/4-(2x-1)^2/16=35/16

$$\frac { ( x - 3 ) ^ { 2 } } { 4 } - \frac { ( 2 x - 1 ) ^ { 2 } } { 16 } = \frac { 35 } { 16 }$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 16, the least common multiple of 4,16.

$$4\left(x-3\right)^{2}-\left(2x-1\right)^{2}=35$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$4\left(x^{2}-6x+9\right)-\left(2x-1\right)^{2}=35$$

Use the distributive property to multiply 4 by x^{2}-6x+9.

$$4x^{2}-24x+36-\left(2x-1\right)^{2}=35$$

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

$$4x^{2}-24x+36-\left(4x^{2}-4x+1\right)=35$$

To find the opposite of 4x^{2}-4x+1, find the opposite of each term.

$$4x^{2}-24x+36-4x^{2}+4x-1=35$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-24x+36+4x-1=35$$

Combine -24x and 4x to get -20x.

$$-20x+36-1=35$$

Subtract 1 from 36 to get 35.

$$-20x+35=35$$

Subtract 35 from both sides.

$$-20x=35-35$$

Subtract 35 from 35 to get 0.

$$-20x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -20 is not equal to 0, x must be equal to 0.

$$x=0$$