So firstly, factor 4x^2 + 32x. Make sure that you leave the x variables in the parentheses: [tex]4(x^2+8x)+70[/tex]
Next, we want to make what's inside the parentheses a perfect square. To find the constant of the perfect square, divide the x coefficient by 2 and square that quotient. In this case:
8 ÷ 2 = 4, 4² = 16
Add 16 to the inside of the parentheses: [tex]4(x^2+8x+16)+70[/tex]
Now to cancel out the 16, we have to subtract the product of 16 and 4 to the outside of the parentheses, which is 64. Subtract 64 on the outside: [tex]4(x^2+8x+16)+70-64\\4(x^2+8x+16)+6[/tex]
Now lastly, factor the perfect square and your answer will be [tex]4(x+4)^2+6[/tex]
