# Khan/khan-exercises

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 Solving quadratics by taking the square root
randRangeNonZero( -10, 10 ) randRange( 1, 9 ) -( CONSTANT * CONSTANT )

Solve for x:

(x - H)^2 + K = 0

H + CONSTANT
H - CONSTANT

x = {}\space \text{or} \space x = {}

integers, like 6

simplified proper fractions, like 3/5

simplified improper fractions, like 7/4

and/or exact decimals, like 0.75

Add abs( K ) to both sides so we can start isolating x on the left:

\qquad (x - H)^2 = -K

Take the square root of both sides to get rid of the exponent.

\qquad \sqrt{(x - H)^2} = \pm \sqrt{-K}

Be sure to consider both positive and negative CONSTANT, since squaring either one results in -K.

\qquad x - H = \pm CONSTANT

Add abs( H ) to both sides to isolate x on the left: Subtract abs( H ) from both sides to isolate x on the left:

\qquad x = H \pm CONSTANT

Add and subtract CONSTANT to find the two possible solutions:

Determine where f(x) intersects the x-axis.

f(x) = (x - H)^2 + K

The function intersects the x-axis where f(x) = 0, so solve the equation:

\qquad (x - H)^2 + K = 0

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