Solve Using the Quadratic Formula 5w^2-3=0

Problem

5*w2−3=0

Solution

1. Identify the coefficients of the quadratic equation in the standard form a*w2+b*w+c=0

a=5

b=0

c=−3

2. State the quadratic formula used to find the roots of the equation.

w=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

w=(−0±√(,0−4*(5)*(−3)))/(2*(5))

4. Simplify the expression inside the square root (the discriminant).

w=(±√(,60))/10

5. Simplify the radical by factoring out the largest perfect square.

w=(±√(,4⋅15))/10

w=(±2√(,15))/10

6. Reduce the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2

w=±√(,15)/5

Final Answer

w=±√(,15)/5

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