Questions: Solve the quadratic inequality. Write the solution set in interval notation. x^2 - 8x ≤ -13

Solve the quadratic inequality. Write the solution set in interval notation. x^2 - 8x ≤ -13
Transcript text: Solve the quadratic inequality. Write the solution set in interval notation. \[ x^{2}-8 x \leq-13 \]
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Solution

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Solution Steps

Step 1: Rearrange the inequality

Rearranged inequality: \(ax^2 + bx + (c-d) \, <= \, 0\)

Step 2: Find the roots of the corresponding quadratic equation

Using the quadratic formula, the roots are: 9.39 and -1.39

Step 3: Determine the sign of the quadratic expression

Based on the sign of \(a\) and the roots, the expression changes sign at: [-1.39, 9.39]

Step 4: Express the solution in interval notation

Considering the type of inequality, the solution set in interval notation is: [-∞, -1.39] ∪ [9.39, ∞]

Final Answer:

[-∞, -1.39] ∪ [9.39, ∞]

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