Question

Represent the solution graphically. Check the solution algebraically. $$ x^{2}+2 x=3 $$

Short answer

The solutions of the equation are x = 1 and x = -3

Step-by-step solution

Rearrange the equation

First, simplify the equation by moving the constant term to one side. So the equation becomes, \(x^{2} + 2x - 3 = 0\)

Plot the function

The function corresponding to the equation is \(y = x^{2} + 2x - 3\). By plotting this function, you will get a parabola and can read its roots from the graph, which are the x-values where the function intersects the x-axis.

Solve for x using the quadratic formula

The quadratic formula is given by \(-\frac{b}{2a} \pm \frac{\sqrt{b^2-4ac}}{2a}\), where a, b and c are coefficients of the quadratic equation. In this case, a = 1, b = 2 and c = -3. Substituting these values into the formula, you find that the solutions are \(x = 1\) and \(x = -3\)

Check the solution algebraically

Substitute the solution back into the original equation to verify. For \(x = 1\), \(1^2 + 2*1 = 3\), which is true. For \(x = -3\), \((-3)^2 + 2*-3 = 3\), which is also true. So, the roots are correct