Question

Solve the Quadratic Equation: X^2+3x=4 Solve by Completing theSquare by following these steps Complete the squarefor the resultingbinomial by adding thesquare of half of thecoefficient of x to bothsides of the equation.Factor the resultingperfect square trinomialand write it as thesquare of a binomial.Use the square rootproperty to solve for x.

Answer 1

Given:

`x^2+3x=4`

Required:

We need to find root by Completing the Square method.

Step-by-step explanation:

`\begin{gathered} x^(2)+3x=4 \\ x^2+3x-4= \\ x^2+2*(3)/(2)x-4=0 \\ \\ x^2+2*(3)/(2)x-((3)/(2))^2+((3)/(2))^2-4=0 \\ \\ (x+(3)/(2))^2=(25)/(4) \\ \\ x+(3)/(2)=\pm(5)/(2) \end{gathered}`

now find the values of x

`\begin{gathered} x=(5)/(2)-(3)/(2)=1 \\ \\ or \\ x=-(5)/(2)-(3)/(2)=-4 \end{gathered}`

Final answer:

Solutions of given equation are x=1 and x=-4