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Solve the following equation for x.
10 = 2 - 4(ar - 3)

1 Answer

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Final answer:

To solve the quadratic equation t² + 10t - 2000 = 0, the quadratic formula t = [-b ± sqrt(b² - 4ac)]/(2a) is applied, yielding two solutions: t = 40 and t = -50.

Step-by-step explanation:

To solve the quadratic equation t² + 10t - 2000 = 0 for t, we will use the quadratic formula. This formula is used to find the solutions for the equation of the form at² + bt + c = 0. The quadratic formula is given by:

t = ∓[-b ± sqrt(b² - 4ac)]/(2a)

For the given equation, a = 1, b = 10, and c = -2000. Substituting these values into the quadratic formula:

t = [-10 ± sqrt(10² - 4(1)(-2000))]/(2 * 1)

t = [-10 ± sqrt(100 + 8000)]/2

t = [-10 ± sqrt(8100)]/2

t = [-10 ± 90]/2

Now, we break it down into two possible solutions:

t = (-10 + 90)/2 = 40

or

t = (-10 - 90)/2 = -50

So, the solutions for the equation t² + 10t - 2000 = 0 are t = 40 and t = -50.

User LinusK
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