Question
Solve the following quadratic equation for all values of x in simplest form.9(5x−8)^2 −5= −1 (simplify into fractions.)
Answers
Answered by
GPT 3.5
First, expand the left side of the equation:
9(5x-8)^2 - 5 = 9(25x^2 - 80x + 64) - 5 = 225x^2 - 720x + 576 - 5 = 225x^2 - 720x + 571
Now, set the equation equal to -1:
225x^2 - 720x + 571 = -1
Simplify by adding 1 to both sides:
225x^2 - 720x + 572 = 0
Divide by 4 to simplify the equation:
56.25x^2 - 180x + 143 = 0
We can't simplify this equation any further without using decimals, so this is the simplest form of the equation.
9(5x-8)^2 - 5 = 9(25x^2 - 80x + 64) - 5 = 225x^2 - 720x + 576 - 5 = 225x^2 - 720x + 571
Now, set the equation equal to -1:
225x^2 - 720x + 571 = -1
Simplify by adding 1 to both sides:
225x^2 - 720x + 572 = 0
Divide by 4 to simplify the equation:
56.25x^2 - 180x + 143 = 0
We can't simplify this equation any further without using decimals, so this is the simplest form of the equation.
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