Mathematics: What is the solution of StartRoot negative 4 x EndRoot = 100?

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What is the solution of StartRoot negative 4 x EndRoot

Chan592

16.03.2022

The given can be solved by simplifying the equation to make x the subject

of the equation.

The solution of the equation is x = -2,500

Reasons:

The equation is; √(-4·x) = 100

The above equation can be expressed as follows;

$\displaystyle \sqrt{-4 \cdot x} = \left(-4 \cdot x \right)^{\frac{1}{2} } = \mathbf{100}$

By squaring both sides, we get;

$\displaystyle \mathbf{ \left(-4 \cdot x \right)^{\frac{1}{2} \times 2 }} = 100^2$

Which gives;

$\displaystyle \left(-4 \cdot x \right)^{\frac{1}{2} \times 2 } = \left(-4 \cdot x \right)^{1 }= -4 \cdot x = 100^2$

$\displaystyle -4 \cdot x = 100^2 = 100 \times 100 = \mathbf{10,000}$

$\displaystyle -4 \cdot x = 10,000$

Dividing both sides by -4 gives;

$\displaystyle x = \mathbf{ \frac{10,000}{-4} } = -2,500$

Therefore'

x = -2,500

The solution of the equation √(-4·x) = 100 is; x = -2,500

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