Answer:
-The solutions are:
[tex]x = 10[/tex]
[tex]x = -2[/tex]
Step-by-step explanation:
-Solve the equation:
[tex](x-3)(x-5) =35[/tex]
-Use Distributive property to multiply the [tex]x -3[/tex] by [tex]x -5[/tex] and combine like terms:
[tex](x-3)(x-5) =35[/tex]
[tex]x^2-8x + 15 = 35[/tex]
-Subtract 35 from 15:
[tex]x^2 - 8x + 15 -35 = 35 -35[/tex]
[tex]x^2 - 8x - 20 =0[/tex]
-Use the quadratic formula and substitute 1 for [tex]a[/tex], -8 for [tex]b[/tex] , and -20 for [tex]c[/tex] :
[tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\frac{-(-8)\pm\sqrt{(-8)^2-4(-20)} }{2}[/tex]
-Simplify the 8 by the exponent 2:
[tex]x = \frac{-(-8)\pm\sqrt{(-8)^2-4(-20)} }{2}[/tex]
[tex]x = \frac{-(-8)\pm\sqrt{64-4(-20)} }{2}[/tex]
-Multiply -20 by -4:
[tex]x = \frac{-(-8)\pm\sqrt{64-4(-20)} }{2}[/tex]
[tex]x = \frac{-(-8)\pm\sqrt{64+80} }{2}[/tex]
-Add both 64 and 80 together:
[tex]x = \frac{-(-8)\pm\sqrt{64+80} }{2}[/tex]
[tex]x = \frac{-(-8)\pm\sqrt{144} }{2}[/tex]
-Take the square root of 144:
[tex]x = \frac{-(-8)\pm\sqrt{144} }{2}[/tex]
[tex]x = \frac{-(-8)\pm 12 }{2}[/tex]
-Change -8 to 8 , because negative and negative equals a positive:
[tex]x = \frac{-(-8)\pm 12 }{2}[/tex]
[tex]x =\frac{8\pm 12 }{2}[/tex]
-Solve the equation when [tex]\pm[/tex] is in addition. So, you would add 8 and 12 together:
[tex]x =\frac{8\pm 12 }{2}[/tex]
[tex]x =\frac{8 + 12 }{2}[/tex]
[tex]x =\frac{20 }{2}[/tex]
-Divide 20 by 2:
[tex]x =\frac{20}{2}[/tex]
[tex]x = 10[/tex]
So, the first answer is [tex]x = 10[/tex].
-To find the second answer, you need to solve the equation when [tex]\pm[/tex] is in subtraction. So, you would subtract both 8 and 12 together:
[tex]x =\frac{8\pm 12 }{2}[/tex]
[tex]x =\frac{8 - 12 }{2}[/tex]
[tex]x = \frac{-4}{2}[/tex]
-Divide -4 by 2:
[tex]x = \frac{-4}{2}[/tex]
[tex]x = -2[/tex]
So, the second answer is [tex]x = -2[/tex] .
The solutions are:
[tex]x = 10[/tex]
[tex]x = -2[/tex]
