4.1-4.4 Solving Equations

Front

What is the first step to solving the equation by completing the square: a^2 + 10a + 21 = 0?

Back

Subtract 21 from both sides to isolate the quadratic expression.

Tags

CCSS.HSA-REI.B.4B

Front

Solve by taking the square root: 2(x-3)^2 + 14 = -18

Back

x = 3 ± 4i

Tags

CCSS.HSA-REI.B.4B

Front

Solve for k: -2(k - 1)^2 - 4 = -36

Back

k = 5, -3

Tags

CCSS.HSA-REI.B.4B

Front

Solve the equation: 4(x + 9)^2 = 24

Back

x = -9 ± √6

Tags

CCSS.HSA-REI.B.4B

Front

Solve: 14m^2 - 12m = 0

Back

m = 0 and m = 6/7

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean to complete the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic in the form (x - p)^2 = q to make it easier to solve.

Tags

CCSS.HSA-REI.B.4B

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a) for the equation ax^2 + bx + c = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is b^2 - 4ac and determines the nature of the roots of the equation.

Tags

CCSS.HSA-REI.B.4B

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable alone on one side of the equation.

Tags

CCSS.7.EE.B.4A

Front

What is the significance of imaginary numbers in solving equations?

Back

Imaginary numbers allow for solutions to equations that do not have real solutions, particularly when taking square roots of negative numbers.