Solve the equation x, squared, minus, 15, x, minus, 39, equals, minus, 30x 2 −15x−39=−30 to the nearest tenth.

Sure, let's solve the equation step by step.

Given equation: $x^2 - 15x - 39 = -30$

Step 1: Move all terms to one side of the equation to set it to zero. $x^2 - 15x - 39 + 30 = 0$ $x^2 - 15x - 9 = 0$

Step 2: Use the quadratic formula to solve for $x$. The quadratic formula is: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a = 1$, $b = -15$, and $c = -9$.

Step 3: Substitute the values of $a$, $b$, and $c$ into the quadratic formula. $x = \frac{-(-15) \pm \sqrt{(-15)^2 - 4(1)(-9)}}{2(1)}$ $x = \frac{15 \pm \sqrt{225 + 36}}{2}$ $x = \frac{15 \pm \sqrt{261}}{2}$

Step 4: Simplify the expression under the square root. $\sqrt{261} \approx 16.2$

Step 5: Substitute back into the formula. $x = \frac{15 \pm 16.2}{2}$

Step 6: Calculate the two possible values for $x$. $x_1 = \frac{15 + 16.2}{2} = \frac{31.2}{2} = 15.6$ $x_2 = \frac{15 - 16.2}{2} = \frac{-1.2}{2} = -0.6$

So, the solutions to the equation $x^2 - 15x - 39 = -30$ to the nearest tenth are: $x \approx 15.6$ $x \approx -0.6$

The given equation is x^2 - 15x - 39 = -30.

First, we need to simplify the equation. We can do this by adding 30 to both sides of the equation to get rid of the negative sign on the right side. This gives us:

x^2 - 15x - 39 + 30 = 0

Simplify further to get:

x^2 - 15x - 9 = 0

Next, we need to solve for x. This is a quadratic equation, so we can use the quadratic formula, which is:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

In this equation, a = 1 (the coefficient of x^2), b = -15 (the coefficient of x), and c = -9.

Substitute these values into the quadratic formula to get:

x = [15 ± sqrt((-15)^2 - 41(-9))] / 2*1 x = [15 ± sqrt(225 - (-36))] / 2 x = [15 ± sqrt(261)] / 2

So the solutions are:

x = [15 + sqrt(261)] / 2 = 17.1 (to the nearest tenth) x = [15 - sqrt(261)] / 2 = -0.1 (to the nearest tenth)

So, the solutions to the equation x^2 - 15x - 39 = -30 are x = 17.1 and x = -0.1.