Practice Objectives
- Demonstrate an understanding of the square root property
- Demonstrate the ability to solve a quadratic equation by completing the square
Practice Solving Quadratic Equations by Completing the Square
Instructions:
Answer 7/10 questions correctly to pass.
Solve each equation by completing the square.
Formatting Notes:
- Fractions can be written using the "/" key
- Negative fractions can be written as -a/b or a/-b
- Any solution that contains a fraction must be simplified
Problem:
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Square Root Property:
- If x and k are complex numbers and x2 = k, then:
- $$x = \sqrt{k} \: \text{or} \: x = -\sqrt{k}$$
Extending the square root property:
- If (ax + b)2 = k, then:
- $$ax + b = \sqrt{k} \: \text{or} \: ax + b = -\sqrt{k}$$
Completing the Square:
$$ax^2 + bx + c = 0$$
- Write the equation in the correct form:
- Move all variable terms to the left side of the equation
- Move all constant terms to the right side of the equation
- Simplify each side by combining any like terms
- In order to complete the square, the coefficient of x2 needs to be 1:
- If a is not 1, divide each side of the equation by a
- Complete the square:
- Multiply the coefficient of x by 1/2 and then square the result
- The coefficient of x is b if a = 1
- The coefficient of x is b/a if a ≠ 1
- Add the square to both sides of the equation
- The left side can now be factored into a binomial squared
- Multiply the coefficient of x by 1/2 and then square the result
- Solve the equation using the square root property
Step-by-Step:
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