Solve 2x^2 = 9x. Round to the nearset tenth.
a) x = 0 or x = -4.5
b) x = 1.5 or x = 3
c) x = 4.5
d) x = 0 or x = 4.5
2x^2 = 9x
x² = 4.5x
x²-4.5x=0
x(x-4.5) = 0
Can you take it from here?
Thanks MathMate
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To solve the equation 2x^2 = 9x, we need to get all the terms on one side of the equation to equal zero.
Step 1: Subtract 9x from both sides to get 2x^2 - 9x = 0.
Step 2: Factor out an x: x(2x - 9) = 0.
Step 3: Apply the zero product property, which states that if a product equals zero, then at least one of the factors must equal zero.
So, we have two possibilities for this equation:
1) x = 0
2) 2x - 9 = 0
For the second equation, solve for x:
2x = 9
Divide both sides by 2:
x = 4.5
Therefore, the solutions to the equation 2x^2 = 9x are x = 0 or x = 4.5.
Now, let's round these solutions to the nearest tenth.
The nearest tenth for 0 is still 0.
The nearest tenth for 4.5 is also 4.5.
So, the rounded solutions to 2x^2 = 9x, rounded to the nearest tenth, are x = 0 or x = 4.5.
The correct option is d) x = 0 or x = 4.5.