Question

solve the equation $x^2 + 10x + 2 = 0$ to the nearest tenth.
answer attempt 1 out of 2
additional solution no solution
$x = $

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, $a=1$, $b=10$, $c=2$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step3: Calculate discriminant

$\Delta = b^2-4ac = 10^2 - 4(1)(2) = 100-8=92$

Step4: Compute square root of discriminant

$\sqrt{92}\approx9.5917$

Step5: Solve for two roots

First root: $x=\frac{-10+9.5917}{2}=\frac{-0.4083}{2}\approx-0.2$
Second root: $x=\frac{-10-9.5917}{2}=\frac{-19.5917}{2}\approx-9.8$

Answer:

$x\approx-0.2$ and $x\approx-9.8$