To complete the square, we need to rearrange the equation to isolate the quadratic term and then take half of the coefficient of the linear term squared.
Starting with the equation x^2 - 22x + 1 = 15, subtracting 1 from both sides gives us x^2 - 22x = 14.
To complete the square, we take half of the coefficient of the linear term, which is -22, and square it to get (-22/2)^2 = 11^2 = 121.
To balance the equation, we add 121 to both sides, resulting in x^2 - 22x + 121 = 14 + 121, or (x-11)^2 = 135.
Now we take the square root of both sides to solve for x, giving us x-11 = ±√135.
Adding 11 to both sides yields x = 11 ± √135.
So, the correct response is x = 11 ± √135.
Complete the square to solve the following quadratic equation: x2−22x+1=15 .(1 point) Responses x=11+14−−√, 11−14−−√ x equals 11 plus Start Root 14 End Root comma 11 minus Start Root 14 End Root x=−11+14−−√, −11−14−−√ x equals negative 11 plus Start Root 14 End Root comma negative 11 minus Start Root 14 End Root x=11+315−−√, 11−315−−√ x equals 11 plus 3 Start Root 15 End Root comma 11 minus 3 Start Root 15 End Root x=−11+315−−√, −11−315−−√
1 answer
1 answer