Questions: Solve the quadratic equation by completing the square. x^2 + 8x = 48 The solution set is .

Solution Steps

Start with the original equation: $$x^{2} + 8x = 48$$ Rearranging gives: $$x^{2} + 8x - 48 = 0$$

To complete the square, take half of the coefficient of $x$ (which is $8$), square it, and add it to both sides. Half of $8$ is $4$, and squaring it gives $16$: $$x^{2} + 8x + 16 = 48 + 16$$ This simplifies to: $$(x + 4)^{2} = 64$$

Now, take the square root of both sides: $$x + 4 = \pm \sqrt{64}$$ This leads to: $$x + 4 = \pm 8$$ Isolating $x$ gives two solutions: $$x = -4 + 8 \quad \text{and} \quad x = -4 - 8$$ Thus, the solutions are: $$x = 4 \quad \text{and} \quad x = -12$$

Final Answer