Q. Which equation has the same solution as x2+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
Simplify Equation: First, we need to simplify the given equation by moving all terms to one side to set the equation equal to zero.x2+9x+6=−7Add 7 to both sides to get:x2+9x+6+7=0x2+9x+13=0
Complete the Square: Now, we need to determine which of the provided equations has the same solution as x2+9x+13=0. To do this, we will complete the square for the given equation to match it to one of the provided options.The first step in completing the square is to find (b/2)2, where b is the coefficient of x. In this case, b=9.(b/2)2=(9/2)2=(4.5)2=20.25
Group and Combine: Next, we add and subtract (2b)2 to the equation x2+9x+13=0 to complete the square.x2+9x+20.25−20.25+13=0Now, group the perfect square trinomial and the constants:(x2+9x+20.25)−20.25+13=0
Write as Binomial: We can now write the perfect square trinomial as a squared binomial:(x+4.5)2−20.25+13=0Combine the constants:(x+4.5)2−7.25=0
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)2−7.25=0.The correct equation that matches this form is:(x+4.5)2=7.25