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.

Explanation:

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

now find the values of x

$\begin{gathered} x=\frac{5}{2}-\frac{3}{2}=1 \\ \\ or \\ x=-\frac{5}{2}-\frac{3}{2}=-4 \end{gathered}$

Final answer:

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