quadratic equation: $5x^2 + 9x - 170 = 0$

Question

I have a problem, my textbook says the solution of $5x^2 + 9x - 170 = 0$ is $5$ but the book didn't describe how it solved the equation. How can I solve this?

Answer 1

According to the quadratic formula $$x_{1,2}=\frac{-9\pm\sqrt{9^2-4\cdot{5}\cdot{(-170)}}}{2\cdot{5}}=\frac{-9\pm\sqrt{3481}}{10}$$ Please continue.

Answer 2

• Hint. $5x^{2} +9x -170 = 5x^{2} -25x + 34x + 170$

Answer 3

for the equation $ax^2+bx+c=0$ we have $\displaystyle x_{1,2}=-\frac{b}{2a}\pm\frac{1}{2a}\sqrt{b^2-4ac}$

Answer 4

Just complete the square: $$ 5x^2+9x−170=0\\ 25x^2+45x−850=0\\ 100x^2+180x−3400=0\\ (10x + 9)^2 - 3481=0 $$ Now as $3481 = 59^2$ this is equivalent to $$ 10x + 9 = \pm 59\\ x = 5 \text{ or } x = -6.8 $$