Question

Use the quadratic formula, x=−b±b2−4ac√2a, to solve the equation −2x2−6x+3=0. Match each step to the correct method for solving the equation.

Answer 1

Answer:

$x=\frac{-3+ \sqrt{15}}{2}\approx0.4365\text{ or}\\x=\frac{-3-\sqrt{15}}{2}\approx-3.4365$

Step-by-step explanation:

So we have the equation:

$-2x^2-6x+3=0$

And we want to solve it using the quadratic formula:

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

First, let's identify our coefficients.

The a is the coefficient in front of the x² term, so a is -2.

b is the coefficient in from of the x term, so b is -6.

And c is the constant so c is 3.

So, substitute:

$x=\frac{-(-6)\pm \sqrt{(-6)^2-4(-2)(3)}}{2(-2)}$

Simplify. -(-6) is just 6. (-6) squared is 36. -4(-2)(3) is +24. And 2(-2) is -4. So:

$x=\frac{6\pm \sqrt{36+24}}{-4}$

Add:

$x=\frac{6\pm \sqrt{60}}{-4}$

Simplify the square root:

$\sqrt{60}=\sqrt{4\cdot 15}=\sqrt{4}\cdot\sqrt{15}=2\sqrt{15}$

So:

$x=\frac{6\pm 2\sqrt{15}}{-4}$

Simplify by dividing everything by 2:

$x=\frac{3\pm \sqrt{15}}{-2}$

Move the negative in the denominator to the numerator:

$x=\frac{-3\pm \sqrt{15}}{2}$

So, our zeros are:

$x=\frac{-3+ \sqrt{15}}{2}\approx0.4365\text{ or}\\x=\frac{-3-\sqrt{15}}{2}\approx-3.4365$

Answer 2

Answer:

Is this -2x plus or minus 2