Question

Solve the equation algebraically. Check the solutions graphically. $$x^{2}+12=48$$

Short answer

The solutions to the equation are \(x = 6\) and \(x = -6\).

Step-by-step solution

Simplifying the given equation

Start by subtracting 12 from both sides of the equation, which simplifies the equation to \(x^2 = 48 - 12 = 36\).

Calculate the square root

Taking square roots on both sides to isolate x we get \(x = ±√{36}\).

Solve for x

We then find our two solutions, \(x = +6\) and \(x = -6\).

Graphical verification

The solutions can be verified by plotting the graph of \(y = x^{2} + 12\). The x-intercepts of this parabola (where y = 0) should be -6 and 6, confirming our algebraic solutions.