Question

Use the complete the square method to solve for X.

(x)=2x² - 9x +10

Answer 1

$$f(x)=2x^2-9x+10$$

$$f(x)=0=>2x^2-9x+10=0$$

$$2(x^2-\dfrac{9}{2}x+5)=0$$

$$x^2-2(\dfrac{9}{4})x+(\dfrac{9}{4})^2-(\dfrac{9}{4})^2+5=0$$

$$(x-\dfrac{9}{4})^2-\dfrac{1}{16}=0$$

$$(x-\dfrac{9}{4}-\dfrac{1}{4})(x-\dfrac{9}{4}+\dfrac{1}{4})=0$$

$$(x-\dfrac{5}{2})(x-2)=0$$

$$x_1=2, x_2=\dfrac{5}{2}$$

$\{2, \ \dfrac{5}{2}\}$