Question

Usando la formula general:

(2x+5)(2x-3)=209

Answer 1

Respuesta:

$CS= {\{7,-8 \}}$

Explicación paso a paso:

Producto notables:

$(x + a)(x + b)={x}^{2}+(a+b)x+ab$

.......

$(2x + 5)(2x - 3) = 209$

${(2x)}^{2} + (5 - 3)2x + (5)( - 3) = 209$

${4x}^{2} + (2)2x - 15 = 209$

${4x}^{2} +4x - 15 = 209$

${4x}^{2} +4x - 15 - 209 = 0$

${4x}^{2} +4x -224 = 0$

$\frac{{4x}^{2} +4x -224}{4} = \frac{0}{4}$

${x}^{2} + x - 56 =0$

${1x}^{2} +1 x - 56 =0$

$a = 1 \: \: \: \: \: \: \: \: \: b = 1 \: \: \: \: \: c = - 56$

Fórmula general:

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x_{1,2}=\frac{-1\pm\sqrt{1^2-4(1)( - 56)}}{2(1)}$

$x_{1,2}=\frac{-1\pm\sqrt{1 + 224}}{2}$

$x_{1,2}=\frac{-1\pm\sqrt{225}}{2}$

$x_{1,2}=\frac{-1\pm15}{2}$

________________________

$x_{1}=\frac{-1 + 15}{2} \: \: \: \: \: \: \: \: \: x_{2}=\frac{-1 - 15}{2}$

$x_{1}=\frac{14}{2} \: \: \: \: \: \: \: \: \: \: \: x_{2}=\frac{-16}{2}$

$x_{1}= 7\: \: \: \: \: \: \: \: \: x_{2}= - 8$

$CS= {\{7,-8 \}}$