Problem 158 - Algebra and Trigonometry

Question

Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.

Step-by-Step Solution

Answer

The solutions to the equation \(x^2+6x+8=0\) using the quadratic formula are \(x=-4, -2\).

Step 1: Identify the values of 'a', 'b', and 'c'

In the given quadratic equation \(x^2+6x+8=0\), 'a' is 1 (the coefficient of \(x^2\)), 'b' is 6 (the coefficient of 'x'), and 'c' is 8.

Step 2: Substitute 'a', 'b' and 'c' into the quadratic formula

Substitute 'a', 'b', and 'c' into the quadratic formula \(-b \pm \sqrt{b^2-4ac}/2a\). This gives \(-6 \pm \sqrt{6^2-4*1*8}/2*1\).

Step 3: Simplify the expression under the square root sign

Simplify the expression inside the square root: \(6^2-4*1*8\) converges to \(36-32\) which equals to 4.

Step 4: Simplify the expression further to calculate 'x'

Insert the simplified value from the previous step into the equation to find 'x': \(-6 \pm \sqrt{4}/2\) gives the solutions \(x=-4, -2\).\