Question

solve each equation, if necessary round to the near
$x^2 + 11x - 26 = 0$

Explanation:

Step1: Identify the quadratic formula

For a quadratic equation \(ax^2 + bx + c = 0\), the solutions are given by \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 1\), \(b = 11\), \(c=-26\).

Step2: Calculate the discriminant

The discriminant \(D=b^2 - 4ac=(11)^2-4\times1\times(-26)=121 + 104 = 225\).

Step3: Find the square root of the discriminant

\(\sqrt{D}=\sqrt{225} = 15\).

Step4: Substitute into the quadratic formula

\(x=\frac{-11\pm15}{2\times1}\). We have two cases:

• Case 1: \(x=\frac{-11 + 15}{2}=\frac{4}{2}=2\)
• Case 2: \(x=\frac{-11-15}{2}=\frac{-26}{2}=-13\)

Answer:

The solutions are \(x = 2\) and \(x=-13\)