A curve has equation y = 4x^2 + 5x + 3. A line has equation y = x + 2. What is the value of x?

First you as both equations are = to y you can make them equal to eachother. 4x² +5x +3 = x+ 2.Then you rearrange the equation to gather all the terms on one side and make the equation = to 0. You minus x from both sides and then minus 2 from both sides to give you :4x²+4x+1 = 0. Then there are two options.The slightly harder but more time efficient way is: you may want to divide each term by 4 to give 4(x² +x +1/4) = 0 then divide both sides by 4 to give x²+x+1/4 = 0. Then find two numbers that add to make 1 and times to make a quarter, which you may be able to see is 1/2. So (x+1/2)²=0 and so x=-1/2.Or you may find it easier to put the values from the equation 4x²+4x+1 = 0 into the quadratic formula (write on whiteboard)to give x= - 1/2.