Question

Find the roots of the following quadratic equation by the quadratic formula.

a) (x+4) (x+5) =2x+3 (x+1) (x+2) ​

Answer 1

Step-by-step explanation:

$(x + 4)(x + 5) = 2x + 3(x + 1)(x + 2)$

${x}^{2} + 9x + 20 = 2x + 3( {x}^{2} + 3x + 2)$

${x}^{2} + 9x - 2x + 20 = 3 {x}^{2} + 9x + 6$

${x}^{2} - 3 {x}^{2} + 9x - 2x - 9x - 6 + 20 = 0$

$- 2 {x}^{2} - 2x + 14 = 0$

$2 {x}^{2} + 2x - 14 = 0$

$x = \frac{ - b - + \sqrt{ {b}^{2} - 4ac} }{2a}$

b=2, a= 2, c= -14

$x = \frac{ - 2 + - \sqrt{ { - 2}^{2} - 4(2)( - 14) } }{2(2)}$

$x = \frac{ - 2 + - \sqrt{ 4 + 112 } }{4}$

$x = \frac{ - 2 + - \sqrt{116} }{4}$

$x = \frac{ - 2 + - \sqrt{4 \times 4 \times 7} }{4}$

$x = \sqrt{7} - \frac{1}{2} \\ x = - \sqrt{7} - \frac{1}{2}$