Solve the Quadratic Equation with Negative Coefficient: -(x+3)^2=4x

Question

Solve the following equation:

$-(x+3)^2=4x$

00:00 Find X

00:03 Use the shortened multiplication formulas

00:15 Substitute appropriate values according to the data and expand the brackets

00:51 Negative times positive is always negative

01:01 Arrange the equation so that one side equals 0

01:09 Collect like terms

01:24 Multiply by negative to convert from negative to positive

01:38 Examine the coefficients

01:50 Use the root formula

02:10 Substitute appropriate values and solve

02:27 Calculate the square and multiplications

02:43 Calculate the square root of 64

02:52 These are the 2 possible solutions (addition, subtraction)

03:06 And this is the solution to the problem

To solve $-(x+3)^2 = 4x$ , follow these steps:

Step 1: Expand the left side: $-(x+3)^2 = -(x^2 + 6x + 9)$ .
Step 2: Distribute the negative sign: $-x^2 - 6x - 9$ .
Step 3: Set the equation by moving terms to the right: $-x^2 - 6x - 9 = 4x$ becomes $-x^2 - 6x - 9 - 4x = 0$ .
Step 4: Simplify to standard quadratic form: $-x^2 - 10x - 9 = 0$ .
Step 5: Applying the quadratic formula where $a = -1$ , $b = -10$ , $c = -9$ :
$x = \frac{-(-10) \pm \sqrt{(-10)^2 - 4 \cdot (-1) \cdot (-9)}}{2 \cdot (-1)}$ .
$x = \frac{10 \pm \sqrt{100 - 36}}{-2}$ .
$x = \frac{10 \pm \sqrt{64}}{-2}$ .
$x = \frac{10 \pm 8}{-2}$ .
Two solutions arise: $x = \frac{10 + 8}{-2} = -9$ and $x = \frac{10 - 8}{-2} = -1$ .

Therefore, the solutions are $x_1 = -1$ and $x_2 = -9$ .

Thus, the correct answer is $\mathbf{x_1=-1,x_2=-9}$ .

$x_1=-1,x_2=-9$