Question

question
solve the equation to the nearest tenth. $-x^2 + 9x - 17 = -3x^2$
answer attempt 1 out of 2
+ additional solution - no solution
$x = $ submit an

Explanation:

Step1: Rearrange to standard quadratic form

Add $3x^2$ to both sides:
$$-x^2 + 9x - 17 + 3x^2 = 0$$
$$2x^2 + 9x - 17 = 0$$

Step2: Identify coefficients for quadratic formula

For $ax^2+bx+c=0$, $a=2$, $b=9$, $c=-17$
Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step3: Calculate discriminant

$$\Delta = b^2-4ac = 9^2 - 4(2)(-17)$$
$$=81 + 136 = 217$$

Step4: Compute roots

$$x=\frac{-9\pm\sqrt{217}}{4}$$
$\sqrt{217}\approx14.73$
First root: $x=\frac{-9+14.73}{4}=\frac{5.73}{4}\approx1.4$
Second root: $x=\frac{-9-14.73}{4}=\frac{-23.73}{4}\approx-5.9$

Answer:

$x \approx 1.4$ and $x \approx -5.9$