document.write( "Question 623441: x2 + (2x + 6)2 = (2x + 9)2 The example given me to showed 36 when binomials were plugged into the Pyth Theorem. Where did it come from?
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Algebra.Com's Answer #392123 by math-vortex(648) $\"\"$ $\"About$

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document.write( "Hi, there-\r
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document.write( "Here is how to solve this Pythagorean Equation for x, and the side lengths of the right triangle.\r
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document.write( "x^2 + (2x+6)^2 = (2x+9)^2\r
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document.write( "This equation represents a right triangle with legs of length, x and 2x+6, and hypotenuse of length
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document.write( "2x+9.\r
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document.write( "Square the two binomials to clear the parentheses.
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document.write( "x^2 + 4x^2 +24x + 36 = 4x^2 +36x + 81\r
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document.write( "Subtract 4x^2 from both sides of the equation.
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document.write( "x^2 +24x + 36 = 36x + 81\r
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document.write( "Subtract 36x from both sides of the equation.
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document.write( "x^2 -12x + 36 = 81\r
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document.write( "Subtract 91 from both sides of the equation.
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document.write( "x^2 -12x -45 = 0\r
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document.write( "Factor this quadratic polynomial. We want two numbers whose product is -45 and whose sum is -12.
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document.write( "The numbers are -15 and 3.\r
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document.write( "(x - 15)(x + 3) = 0
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document.write( "x - 15 = 0  OR x + 3 = 0
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document.write( "x = 15   OR x = -3\r
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document.write( "Both these values for x make the original equation true, but x = -3 does not make sense if we are
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document.write( "talking about side lengths of triangles (you can't have a triangle with a side length of -3.)\r
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document.write( "Therefore, x = 15.
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document.write( "2x + 6 = 2(15) +6 = 36.
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document.write( "2x + 9 = 2(15) + 9 = 39.\r
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document.write( "The legs of the right triangle have lengths 15 and 36. (This is where the 36 came from!) The
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document.write( "hypotenuse has a length of 39.\r
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document.write( "Hope this helps. Feel free to email me if you have questions about this,
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document.write( "Ms.Figgy
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document.write( "math.in.the.vortex@gmail.com \n" );
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