# Solving Word Problems With Quadratic Equations

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The standard form of a quadratic equation is ax² bx c.

To solve this problem, we just need 2 important concepts about quadratic equations.

Find the number of girls present in the Sports Meet.

In the Annual Sports Meet in a girls’ school, the girls present in the meet, when arranged in a solid square has 16 girls less in the front row, than when arranged in a hollow square 4 deep.

(Hint: The ratio of the sound intensity is equal to the square of the ratio of their corresponding distances).

Solution There is a square field whose side is 10 m.Step IV: Solve this equation to obtain the value of the unknown in the set to which it belongs.x = -5 does not satisfy the conditions of the problem length or breadth can never be negative. In solving a problem, each root of the quadratic equation is to be verified whether it satisfies the conditions of the given problem. Note that the second value could have been gotten by changing the sign on the extraneous solution.Therefore, from the question,$$\frac$$ $$\frac$$ = 6⟹ $$\frac$$ $$\frac$$ = 6⟹ $$\frac$$ $$\frac$$ = 3⟹ $$\frac$$ = 3⟹ $$\frac$$ = 3⟹ $$\frac$$ = 1⟹ 10x 5 = 4x$$^$$ – 9⟹ 4x$$^$$ – 10x – 14 = 0⟹ 2x$$^$$ -5x – 7 = 0⟹ 2x$$^$$ - 7x 2x - 7= 0⟹ x(2x - 7) 1(2x - 7) = 0⟹ (2x - 7)(x 1) = 0⟹ 2x - 7 = 0 or x 1 = 0⟹ x = $$\frac$$ or x = -1But speed cannot be negative.So, x = $$\frac$$ = 3.5Therefore, the speed of the board in still water is 3.5 km/h.Then, the speed of the boat up the stream (or against the stream) = (x - $$\frac$$) km/hour, and the speed of the boat down the stream (or along the stream) = (x $$\frac$$) km/hour.Therefore, time taken to travel 10 km up the stream = $$\frac$$ hours and time taken to travel 5 km down the stream = $$\frac$$ hours.Warning: Many students get in the very bad habit of arbitrarily changing signs to get the answers they need, but this does not always work, and will very likely get them in trouble later on.Take the extra half a second to find the right answer the right way.As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more.Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

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