Problem 171
Question
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Any quadratic equation that can be solved by completing the square can be solved by the quadratic formula.
Step-by-Step Solution
Verified Answer
The given statement is true. Every quadratic equation that can be solved by completing the square can be solved by the quadratic formula.
1Step 1: Understand the relationship between 'Completing the Square' and the 'Quadratic Formula'
Observe that the process of deriving the quadratic formula involves completing the square. Given any quadratic equation in the form \(ax^2 + bx + c = 0\), the quadratic formula (\(-b ± √(b^2 - 4ac) / 2a\)) is derived by completing the square.
2Step 2: Evaluate the statement
Given this relationship, it can be deduced that if a quadratic equation can be solved by completing the square, it can certainly be solved by the quadratic formula. Hence, the statement is true.
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