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There are two distinct solutions x to the equation 18 + 5x^2 = 30x. If each solution is rounded to the nearest integer, and then these two integers are multiplied together, what is the result?

Nov 30, 2020

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There are two distinct solutions x to the equation 18 + 5x^2 = 30x. If each solution is rounded to the nearest integer, and then these two integers are multiplied together, what is the result?

Hello Guest!

$$18 + 5x^2 = 30x\\ 5x^2-30x+18=0$$

a          b           c

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

$$x = {30 \pm \sqrt{900-4\cdot 5\cdot 18} \over 2\cdot 5}\\ x=\frac{30\pm \sqrt{540}}{10}\\ x_1=5.32379\approx5\\ x_2=0.67621\approx 1$$

$$x_1\cdot x_2\approx5\cdot 1\\ \color{blue}x_1\cdot x_2\approx5$$

!

Nov 30, 2020