Solving Quadratic Equations by Square Roots

The video tutorial covers solving quadratic equations, focusing on special forms and perfect square binomials. It demonstrates solving without factoring by using square roots and compares it with traditional factoring methods. The tutorial prepares viewers for the next lesson on completing the square.

What is the first step in solving the equation 4x + 1 squared minus 8 equals 0?

• Multiply out the expression

• Subtract 8 from both sides

• Add 8 to both sides

• Factor the expression

After adding 8 to both sides of the equation 4x + 1 squared minus 8 equals 0, what is the next step?

• Subtract 1 from both sides

• Take the square root of both sides

• Multiply both sides by 4

• Divide both sides by 4

Why do we consider both the positive and negative square roots when solving 4x + 1 squared equals 8?

• To check for errors

• Because the square root function is undefined

• To simplify the equation

• To account for both possible solutions

What is the simplified form of the equation 4x + 1 equals plus or minus 2 times the square root of 2?

• 4x + 1 equals 2

• 4x + 1 equals plus or minus 2

• 4x + 1 equals 4 times the square root of 2

• 4x + 1 equals plus or minus 2 times the square root of 2

What is the final step in solving for x in the equation 4x equals negative 1 plus or minus 2 times the square root of 2?

• Add 1 to both sides

• Multiply both sides by 4

• Divide both sides by 4

• Subtract 1 from both sides

What is the purpose of substituting the solution back into the original equation?

• To eliminate variables

• To verify the solution

• To find a new solution

• To simplify the equation

In the equation x squared minus 10x plus 25 equals 9, what is the first step to recognize it as a perfect square?

• Inspect the equation for a perfect square

• Subtract 9 from both sides

• Add 9 to both sides

• Factor the equation

What is the factored form of x squared minus 10x plus 25?

• x minus 5 squared

• x plus 5 squared

• x plus 10 squared

• x minus 10 squared

What are the solutions to the equation x minus 5 squared equals 9?

• x equals 5 plus or minus 1

• x equals 5 plus or minus 3

• x equals 5 plus or minus 2

• x equals 5 plus or minus 9

In the final example, what is the factored form of x squared plus 18x plus 81?

• x minus 18 squared

• x minus 9 squared

• x plus 18 squared

• x plus 9 squared