Answer: x = 4.87 .
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A = L * w ;
(Area = Length * width )
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Given: Area = 288 in² .
Length = (2x + 10) in
Width = (3x) in
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A = L * w ;
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288 = (2x + 10) * (3x) ;
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Solve for "x" ;
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Write as:
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(3x)*(2x + 10) = 288 ;
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Note the distributive property of multiplication:
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a(b+c) = ab + ac ; and:
a(b−c) = ab − ac ;
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So;
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(3x)*(2x + 10) =
(3x)*(2x) + (3x)*(10) =
6x² + 30x = 288 ;
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Subtract "288" from each side of the equation:
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6x² + 30x − 288 = 288 − 288 ;
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6x² + 30x − 288 = 0 ;
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Now, divide the ENTIRE equation by "6";
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{6x² + 30x − 288} / 6 = 0 / 6 ;
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x² + 5x − 48 = 0 ;
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We can solve for "x" using the quadratic formula;
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Note, this equation:
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x² + 5x − 48 = 0 ; is written is "quadratic format"; that is:
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ax² + bx + c = 0 ; a ≠ 0 ;
in which:
a = 1 (the implied coefficient of "1", since anything multiplied by "1" is that same value);
b = 5 ;
c = -48 ;
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and we can solve for "x" using the quadratic equation formula; which is:
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x = { -b ± √(b² − 4ac) } / {2a} ; a ≠ 0 ;
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So, we can plug in the values:
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First, let's simplify: "(b² − 4ac)" ; which is:
5² − 4*1*(-48) = 25 − (-192) = 25 + 192 = 217 ;
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So, x = -5 ± √(217) / (2*1) ;
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x = { -5 ± √(217) } / 2 ;
So, there are 2 (TWO) values:
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Start with:
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x = { -5 + √(217) } / 2 = 4.8654599313281177
then, { -5 − √(217) } / 2 = -19.7309198626562354
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Since we are dealing with a rectangle, the answer is the positive value; that is: 4.8654599313281177 ; the question asks to round to the nearest hundredth, if necessary; so; → 4.87 = x .
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