Complete the following questions to practice the skills you have learned in this lesson.
- The quadratic equation is in the form of .
- What is the value of ?
- What is the value of ?
- What is the value of ?
Examine the solution method that has been started below and use it to answer parts d and e.
Original equation
Step 1 - Subtract 10 from each side.
Step 2 - Multiply each side by 4.
Step 3 - Rewrite as and as .
Step 4 -
Step 5 -
Step 6 -
Step 7 -
- In Step 2, what might be a good reason for multiplying each side of the equation by 4?
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Multiplying by 4 makes the coefficient of the squared term a perfect square, which makes it easier to complete the square.
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Multiplying by 4 makes the coefficient of the term a perfect square, which makes it easier to complete the square.
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If the value of is positive and you multiply by 4, it will be easier to divide the term by 3 before you square it.
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You must always multiply both sides by 4 when completing the square.
- Complete the unfinished steps, then select two solutions.
- -10
- -5
- -2
- -4
- Substitute the values of , , and into the quadratic formula, , but do not evaluate any of the expressions. Explain how this expression is related to solving by completing the square.
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For this equation, the quadratic formula and completing the square are not the same and therefore not related.
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They are related because neither one can have a negative value.
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Rather than evaluating at each step, the calculation is done all at once, at the end.
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In both forms of solving the equation, you need to list the values of , , and to determine the solutions.
- Consider the standard form of the equation .
- What is the value of ?
- What is the value of ?
- What is the value of ?
- Can you use the quadratic formula to solve this equation?
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No
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Yes
- Can you solve this equation using square roots?
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No, this equation can only be solved by the quadratic formula.
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Yes, the solutions are .
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No, there is no solution.
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Yes, the solutions are .
- Clare is deriving the quadratic formula by solving by completing the square.
She arrived at this equation: .
Choose the best description of what she needs to do to finish solving for .
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Find the square roots of each side. Divide each side by 2. Subtract from each side.
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Divide each side by 2. Subtract from each side. Then find the square roots of each side.
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Find the square roots of each side. Subtract from each side. Then divide each side by .
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Subtract from each side. Find the square roots of each side. Then divide each side by 2.