What is the first step in solving the quadratic equation [tex]$-5 x^2+8=133$[/tex]?
A. taking the square root of both sides of the equation
B. subtracting 8 from both sides of the equation
C. squaring both sides of the equation
D. adding 8 to both sides of the equation
Answer (2)
Subtract 8 from both sides of the equation: − 5 x 2 + 8 − 8 = 133 − 8 .
Simplify the equation: − 5 x 2 = 125 .
Divide both sides by -5: x 2 = − 25 .
The first step is subtracting 8 from both sides of the equation: s u b t r a c t in g 8 f ro m b o t h s i d es o f t h e e q u a t i o n .
Explanation
Analyze the Problem We are given the quadratic equation − 5 x 2 + 8 = 133 and asked to identify the first step in solving for x . The options are:
taking the square root of both sides of the equation
subtracting 8 from both sides of the equation
squaring both sides of the equation
adding 8 to both sides of the equation
To solve for x , we need to isolate the term with x . This involves performing addition or subtraction to both sides of the equation.
Subtract 8 from both sides To isolate the term with x , we need to subtract 8 from both sides of the equation: − 5 x 2 + 8 − 8 = 133 − 8 This simplifies to: − 5 x 2 = 125
Divide by -5 The next step would be to divide both sides by -5: − 5 − 5 x 2 = − 5 125 x 2 = − 25
Take the square root Finally, we would take the square root of both sides: x = ± − 25
Conclusion Therefore, the first step in solving the quadratic equation − 5 x 2 + 8 = 133 is to subtract 8 from both sides of the equation.
Examples
Consider a scenario where you're trying to determine the initial velocity of an object thrown upwards. The equation might involve a quadratic term representing the effect of gravity. Before you can isolate the velocity variable, you need to simplify the equation by subtracting any constant terms from both sides. This is analogous to the first step in solving the given quadratic equation, where subtracting 8 from both sides helps isolate the term containing the variable.
The first step in solving the quadratic equation − 5 x 2 + 8 = 133 is to subtract 8 from both sides of the equation. This step isolates the term with the variable x , leading to − 5 x 2 = 125 . Thus, the correct answer is option B.
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