Question

current learning objective: using the quadratic formula
question 6
score: 0 of 1 point
the equation x² + 4x - 14 = 0 has two solutions a and b where a < b.
a = enter your answer and
b = enter your answer
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Explanation:

Step1: Identify coefficients

For the quadratic equation $x^{2}+4x - 14=0$, we have $a = 1$, $b = 4$, $c=-14$.

Step2: Apply quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values: $x=\frac{-4\pm\sqrt{4^{2}-4\times1\times(-14)}}{2\times1}=\frac{-4\pm\sqrt{16 + 56}}{2}=\frac{-4\pm\sqrt{72}}{2}=\frac{-4\pm6\sqrt{2}}{2}=-2\pm3\sqrt{2}$.

Step3: Find A and B

Since $A < B$, $A=-2 - 3\sqrt{2}$ and $B=-2 + 3\sqrt{2}$.

Answer:

$A=-2 - 3\sqrt{2}$
$B=-2 + 3\sqrt{2}$