Question

Solve for x in the equation.

Answer 1

Answer:

The solution is $\displaystyle x=1\pm \sqrt{47}$. Fourth option

Explanation:

Solve for x:

$2x^2+3x-7=x^2+5x+39$

Move all the terms from the right to the left side of the equation, a zero in the right side:

$2x^2+3x-7-x^2-5x-39=0$

Join all like terms:

$x^2-2x-46=0$

The general form of the quadratic equation is:

$ax^2+bx+c=0$

Solve the quadratic equation by using the formula:

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

In our equation: a=1, b=-2, c=-46

Substituting into the formula:

$\displaystyle x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-46)}}{2(1)}$

$\displaystyle x=\frac{2\pm \sqrt{4+184}}{2}$

$\displaystyle x=\frac{2\pm \sqrt{188}}{2}$

Since 188=4*47

$\displaystyle x=\frac{2\pm \sqrt{4*47}}{2}$

Take the square root of 4:

$\displaystyle x=\frac{2\pm 2\sqrt{47}}{2}$

Divide by 2:

$\displaystyle x=1\pm \sqrt{47}$

First option: Incorrect. The answer does not match

Second option: Incorrect. The answer does not match

Third option: Incorrect. The answer does not match

Fourth option: Correct. The answer matches exactly this option