Exploring Adding and Subtracting Rational Expressions

What are the solutions for the equation x^2 - 6x - 40 = 0 when solved by factoring?

• x = -5, -8

• x = 5, 8

• x = 4, -10

• x = -4, 10

For the equation 10x^2 - 25 = x^2, what method is used to solve it?

• Quadratic formula

• Factoring

• Square roots

• Completing the square

What is the solution for the equation 2x^2 + 80 = 26x when solved by factoring?

• x = -5, -8

• x = -4, -10

• x = 5, 8

• x = 4, 10

What is the first step in solving quadratic equations by factoring?

• Find the square root of the leading coefficient

• Divide each term by the leading coefficient

• Ensure the equation is set to equal zero

• Identify the factors of the constant term

What is the purpose of isolating x^2 when solving quadratic equations using the square roots method?

• To prepare for square rooting both sides

• To simplify the equation

• To complete the square

• To factor the equation

What is the 'magic number' in the context of completing the square?

• Half of the coefficient of x, squared

• The coefficient of x

• The constant term

• Half of the coefficient of x squared

What are the solutions for the equation x^2 - 18x + 65 = 0 using the completing the square method?

• x = 5, 13

• x = -5, -13

• x = -4, -16

• x = 4, 16

For the equation 9x^2 - 18x = 40, what is the first step in solving it by completing the square?

• Divide by 9

• Subtract 40

• Add 18x to both sides

• Factor out the greatest common factor

What is the correct formula for the quadratic formula method?

• x = b ± sqrt(b^2 + 4ac) / 2a

• x = -b ± sqrt(b^2 - 4ac) / 2a

• x = b ± sqrt(b^2 - 4ac) / 2

• x = -b ± sqrt(b^2 + 4ac) / 2

What is the simplified form of the solution for the equation x^2 + 12x - 24 = 0 using the quadratic formula?

• x = -6 ± 2sqrt(15)

• x = 6 ± 2sqrt(15)

• x = 6 ± sqrt(15)

• x = -6 ± sqrt(15)