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.

Front

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

Back

x = 3 ± 4i

Front

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

Back

k = 5, -3

Front

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

Back

x = -9 ± √6

Front

Solve: 14m^2 - 12m = 0

Back

m = 0 and m = 6/7

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.

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.

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.

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.

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.