Question

Find the value of x that will solve the equation. 9x^2+25=0. Please show work.

Answer 1

x = ±(5/3)i

Explanation:

- Consider a general quadratic equation ax² + bx + c = 0

- Using the bulldozer method;

`{ \tt{x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac } }{2a} }} \\`

- Relating 9x² + 25 = 0

• a is 9
• b is 0
• c is 25

`{ \tt{x = \frac{ - 0 \pm \sqrt{ {0}^(2) - (4 * 9 * 25)} }{(2 * 9)} }} \\ \\ { \tt{x = ( √( - 900) )/(18) }} \\ \\ { \tt{x = ( √( - 1 * 900) )/(18) }}`

- From complex numbers, -1 = i²

`{ \tt{x = \frac{ \sqrt{ {i}^(2) * 900} }{18} }} \\ \\ { \tt{x = (30i)/(18) }} \\ \\ { \tt{x = \pm (5)/(3)i }}`

Or:

`{ \tt{9 {x}^(2) + 25 = 0 }} \\ { \tt{9 {x}^(2) = - 25}} \\ \\ { \tt{ √(x)^(2) = \sqrt{ - (25)/(9) } }} \\ \\ { \tt{x = √( - 1) * ( √(25) )/( √(9) ) }} \\ \\ { \tt{x = \sqrt{ {i}^(2) } * (5)/(3) }} \\ \\ { \tt{x = \pm(5)/(3) i}}`

Answer 2

`\sf x = + (5)/(3)i ; \ (-5)/(3)i`

Explanation:

Solving the equation:

9x² + 25 = 0

9x² = -25

`\sf x^2= (-25)/(9)\\\\ i^2 = -1 \\\\x^2=(25)/(9)i^2\\\\x=\sqrt{(25)/(9)i^2}\\\\`

`\sf x = \± (5)/(3)i`