# Quadratic equations and inequalities

Solve each equation:

1) 2y^2 - 3y -6 = 0

2) (x-10)(x-2) = -20

Find all real or imaginary solutions for each equation:

1) W^2=-225

2) 3v^2+4v-1=0

3) sqrt (7x+29) = x+3

Word Problem

Time to Swing. The period T (time in seconds for one complete cycle) of simple pendulum is related to the length L (in feet) of the pendulum by the formula 8T^2=(pi)^2L. If a child is on a swing with a 10-foot chain, then how long does it take to complete one cycle of the swing?

NOTE:

Please help me better understand the above. I am having a hard time with the concept and I am note sure my answers are correct. Thank you so much for all your help.

https://brainmass.com/math/basic-algebra/quadratic-equations-inequalities-148885

#### Solution Preview

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Note: I am using the formula for the solution of a quadratic equation.

Solutions of a quadratic equation of the form ax^2 + bx + c = 0 is given by:

x = [-b +/- sqrt(b^2 - ...

#### Solution Summary

I have solved five problems involving solutions to quadratic equations and one word problem. Solution is well written with clear steps.