Solve x^2 + x/2 =5

Although this may look more complicated than normal, this is just a normal qudratic equation. First by rearranging the equation we can get it into a simpler form, and then we can go about solving it. The first thing to remember is whatever operation you apply to one side of the equation, you must do to the other! So first of all, we can multiply the whole equation by 2 to get simplify the x/2 term. The equation becomes: 2x^2 +x=10 Now we can subtract 10 from both sides, to bring all of the terms to one side. The equation becomes: 2x^2 +x -10=0 This is now much nicer to work with! Now to solve the equation, we can use two methods. We can either use the quadratic formula (whereby we plug all of the coefficients into the equation to find the roots) or we can factorise it. Luckily this equation factorises nicely into: (x-2)(2x+5)=0 Since one of the brackets must equal 0, this gives the solutions: x=-5/2 or x=2