what are the solutions to the following equations?

Question

4x^2+13x=12


x^2+6x+16=0

Answer 1

4x² + 13x = 12

4x² + 13x - 12 = 12 - 12

4x² + 13x - 12 = 0

Find the sum of the middle term

Multiply the first term 4 times the last term 8 = 48 and factor

4 x 12 = 48

factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

16 - 3 satisfy the sum of the middle term

4x² - 13x - 12

4x² + 16x - 3x - 12 = 0

4x(x + 4) - 3(x + 4)

(4x - 3)(x + 4)

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x² + 6x + 16

The value of the first term = 1

find the sum of the middle term

Multiply the first term times the last term16 and factor

1 x 16 = 16

Factors of 16 = 1, 2, 4, 8, 16

8 - 2 satisfy the sum of the middle term

x² + 8x - 2x + 16 = 0

x(x + 8) - 2(x + 8) = 0

(x - 2)(x + 8) = 0

- - - - - - - - - -s-

Answer 2

1)u can use the equation:
the solutions to the equation ax^2+bx+c=0
are
x=(-b+sqrt(b^2-4ac))/2a
or x=(-b-sqrt(b^2-4ac))/2a

4x^2+13x=12
4x^2+13x-12=0

here a=4, b=13,c=-12,from there u just use the equation.



2)x^2+6x+16=0
a=1,b=6,c=16

u can finish the rest yourself

Answer 3

if I read it correctly it's 4x² + 13x = 12 and x²+6x+16=0
there is a rule that says (a + b)² = a² + 2ab + b²

are you really sure that this is the correct exersice because to me it's impossible to find a solution and i know that the rule above is the correct one...

sorry can't help further...

Answer 4

4x^2 +13x -12 = 0
x = (-13 +/-sqrt(169 + 192))/8
x =(-13 +/- sqrt(361))/8
x = (-13 +/- 19)/8
x = -4 and x = 3/4

x^2 + 6x + 16 = 0
x =(-6 +/- sqrt(36 -64))/2
x =(-6 +/- sqrt(-28))/2
x =(-6 +/- 5.29 i)/2
x =-11.29i/2 and x=-0.71i/2
x = -5.64i and x = -0.36i

Answer 5

The first equation is either .75 or -4.

The second equation cannot be solved using real numbers.....