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Quadratic Equations: A Worked Example with a Rectangle

Learn how to solve a quadratic equation by considering the area of a rectangle given by A = x(x+7). Follow a step-by-step process to find x when solving x^2 + 7x - 67 = 0. Understand the quadratic equation formula for a clearer solution.

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Quadratic Equations: A Worked Example with a Rectangle

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  1. Quadratic Equations A worked example

  2. 67 x x+7 • Consider the rectangle below • The area of the rectangle is given by A = x(x+7) So we now obtain the equation x(x+7) = 67 This simplifies to give x2 + 7x - 67 = 0 , on moving all the terms to one side of the equation.

  3. To solve this equation we use the quadratic equation • So we have a = 1 , b = 7 and c = - 67. • This gives

  4. This simplifies to • Which leads to • So • Giving the two solutions x = 5.40 and -12.40

  5. Now x -12.40 as you cannot have a negative length of side so we are left with the solution that x = 5.40

  6. 93 x+3 37 x+2 x+8 x+4 • Find x in each of the examples below. 1. 2.

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