Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which equation has the same solution as 
x^(2)+9x+6=-7 ?

(x+4.5)^(2)=-33.25

(x-4.5)^(2)=7.25

(x+4.5)^(2)=7.25

(x-4.5)^(2)=-33.25

Which equation has the same solution as x2+9x+6=7 x^{2}+9 x+6=-7 ?\newline(x+4.5)2=33.25 (x+4.5)^{2}=-33.25 \newline(x4.5)2=7.25 (x-4.5)^{2}=7.25 \newline(x+4.5)2=7.25 (x+4.5)^{2}=7.25 \newline(x4.5)2=33.25 (x-4.5)^{2}=-33.25

Full solution

Q. Which equation has the same solution as x2+9x+6=7 x^{2}+9 x+6=-7 ?\newline(x+4.5)2=33.25 (x+4.5)^{2}=-33.25 \newline(x4.5)2=7.25 (x-4.5)^{2}=7.25 \newline(x+4.5)2=7.25 (x+4.5)^{2}=7.25 \newline(x4.5)2=33.25 (x-4.5)^{2}=-33.25
  1. Simplify Equation: First, we need to simplify the given equation by moving all terms to one side to set the equation equal to zero.\newlinex2+9x+6=7x^2 + 9x + 6 = -7\newlineAdd 77 to both sides to get:\newlinex2+9x+6+7=0x^2 + 9x + 6 + 7 = 0\newlinex2+9x+13=0x^2 + 9x + 13 = 0
  2. Complete the Square: Now, we need to determine which of the provided equations has the same solution as x2+9x+13=0x^2 + 9x + 13 = 0. To do this, we will complete the square for the given equation to match it to one of the provided options.\newlineThe first step in completing the square is to find (b/2)2(b/2)^2, where bb is the coefficient of xx. In this case, b=9b = 9.\newline(b/2)2=(9/2)2=(4.5)2=20.25(b/2)^2 = (9/2)^2 = (4.5)^2 = 20.25
  3. Group and Combine: Next, we add and subtract (b2)2(\frac{b}{2})^2 to the equation x2+9x+13=0x^2 + 9x + 13 = 0 to complete the square.\newlinex2+9x+20.2520.25+13=0x^2 + 9x + 20.25 - 20.25 + 13 = 0\newlineNow, group the perfect square trinomial and the constants:\newline(x2+9x+20.25)20.25+13=0(x^2 + 9x + 20.25) - 20.25 + 13 = 0
  4. Write as Binomial: We can now write the perfect square trinomial as a squared binomial:\newline(x+4.5)220.25+13=0(x + 4.5)^2 - 20.25 + 13 = 0\newlineCombine the constants:\newline(x+4.5)27.25=0(x + 4.5)^2 - 7.25 = 0
  5. Match to Equation: Finally, we need to find an equation that matches the form of our completed square equation. We are looking for an equation that has the same solution as (x+4.5)27.25=0(x + 4.5)^2 - 7.25 = 0.\newlineThe correct equation that matches this form is:\newline(x+4.5)2=7.25(x + 4.5)^2 = 7.25

More problems from Transformations of functions