find a positive real number such that its square is equal to 15 times the number increased by 286

Accepted Solution

Answer:The positive real number is 26Step-by-step explanation:Letx ----> the numberwe know thatThe algebraic expression that represent this problem is [tex]x^{2} =15x+286[/tex]so[tex]x^{2}-15x-286=0[/tex]The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to [tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex] in this problem we have [tex]x^{2}-15x-286=0[/tex]so [tex]a=1\\b=-15\\c=-286[/tex] substitute in the formula [tex]x=\frac{-(-15)(+/-)\sqrt{-15^{2}-4(1)(-286)}} {2(1)}[/tex] [tex]x=\frac{15(+/-)\sqrt{1,369}} {2}[/tex] [tex]x=\frac{15(+/-)37}{2}[/tex] [tex]x_1=\frac{15(+)37}{2}=26[/tex] [tex]x_2=\frac{15(-)37}{2}=-11[/tex] Β ---> the solution cannot be negativethereforeThe positive real number is 26