Question

Determina los valores de a,b y c de las siguientes ecuaciones y resuelve usando la fórmula general. (ax²+b+c=0)

•2x²+2x+3=0
•5x²+2x=0
•36x-x²=62
4x²-6x+2=0
x²+4x=-3
-x²-4x-32=0
-2x²-8x+10=0 ​

Answer 1

Respuesta:

1. 2x²+2x+3=0
2. 5x²+2x=0
3. 36x-x²=62
4. 4x²-6x+2=0
5. x²+4x=-3
6. -x²-4x-32=0
7. -2x²-8x+10=0 ​

Explicación paso a paso:

1. $2x^{2} +2x+3=0$

$2x^{2} +2x=-3$

$x^{2} +x=-\frac{3}{2}$

$x^{2} +x+\frac{1}{4}=-\frac{3}{2}+\frac{1}{4}$

$(x+\frac{1}{2} )^{2} = -\frac{5}{4}$

$x1=-\frac{1}{2}-\frac{\sqrt{5} }{2}i \\ x2=-\frac{1}{2}+\frac{\sqrt{5} }{2}i$

2. $5x^{2}+2x=0$

$x(5x+2)=0$

$x=0\\5x+2=0$

$x1=-\frac{2}{5}\\x2=0$

3. $36x-x^{2} =62$

$-x^{2} +36x=62$

$x^{2} -36x=-62$

$x^{2} -36x+324=-62+324$

$(x-18)^{2} =262$

$x1=-\sqrt{262}+18\\x2=\sqrt{262}+18$

4.$4x^{2} -6x+2=0$

$2x^{2} -3x+1=0$

$2x^{2} -x-2x+1=0$

$x(2x-1)-(2x-1)=0$

$(2x-1)*(x-1)=0$

$x1=\frac{1}{2} \\x2=1$

5. $x^{2} +4x=-3$

$x^{2} +4x+3=0$

$x^{2} +3x+x+3=0$

$x(x+3)+x+3=0$

$(x+3)*(x+1)=0$

$x1=-3\\x2=-1$

6. $-x^{2} -4x-32=0$

$-x^{2} -4x=32$

$x^{2} +4x=-32$

$x^{2} +4x+4=-32+4$

$(x+2)^{2} =-28$

$x1=-2-2\sqrt{7} i\\x2=-2+2\sqrt{7}i$

7.$-2x^{2} -8x+10=0$

$x^{2} +4x-5=0$

$x^{2} +5x-x-5=0$

$x(x+5)-(x+5)=0$

$(x+5)*(x-1)=0$

$x1=-5\\x2=1$