Extracting Square Roots: Applying the formula

First, we move the terms to one side equal to 0.

$2x^2-x^2-8-4=0$

We simplify :

$x^2-12=0$

We use the shortcut multiplication formula to solve:

$x^2-(\sqrt{12})^2=0$

$(x-\sqrt{12})(x+\sqrt{12})=0$

$x=\pm\sqrt{12}$

To solve this quadratic equation $x^2 - 20 = 5$, we will follow these steps:

• Step 1: First, add 20 to both sides of the equation to isolate the $x^2$ term:

$x^2 - 20 + 20 = 5 + 20$

This simplifies to:

$x^2 = 25$

• Step 2: Next, take the square root of both sides to solve for $x$:

$x = \pm \sqrt{25}$

$x = \pm 5$

Therefore, the solutions to the equation are:

$x = 5$ and $x = -5$

Thus, the correct answer choice is:

• $\pm 5$ from the provided options.

The correct solution to the problem is $\pm 5$.

We first rearrange and then set the equations to equal zero.

$x^2-49=0$

$x^2-7^2=0$

We use the abbreviated multiplication formula:

$(x-7)(x+7)=0$

$x=\pm7$

To solve this problem, we'll follow these steps:

• Simplify the given equation.
• Solve for $x^2$ and find $x$.

First, let's simplify the equation:

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

Combine like terms on the left side:

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

Subtract $x^2$ from both sides to isolate one of the $x$ terms:

$2x^2 - x^2 - 3 = 6$.

This simplifies to:

$x^2 - 3 = 6$.

Next, add 3 to both sides to solve for $x^2$:

$x^2 = 9$.

To find $x$, take the square root of both sides:

$x = \pm\sqrt{9}$.

This results in:

$x = \pm3$.

Therefore, the solution to the problem is $\pm3$.

To solve this problem, we'll follow these steps:

• Step 1: Simplify both sides of the equation.
• Step 2: Rearrange terms to form a quadratic equation.
• Step 3: Solve the quadratic equation using an appropriate method, such as factoring or applying the quadratic formula.

Now, let's work through each step:

Step 1: Simplify both sides of the equation:

The right-hand side can be simplified:

This yields the equation:

Step 2: Rearrange the terms to form a quadratic equation. Subtract $2x + 12$ from both sides:

Combining like terms gives:

Step 3: Solve the resulting quadratic equation:

First, we add 4 to both sides:

Next, divide both sides by 4:

Now, apply the square root to both sides:

Therefore, the solutions to the quadratic equation are

$x = \pm 1$.

The correct answer is choice 2: ±1.

Let's solve the equation step-by-step:

• Step 1: Rearrange the equation.

We start with the given equation:

$2x^2 - 8 = x^2 + 4$

Subtract $x^2 + 4$ from both sides to get:

$2x^2 - 8 - x^2 - 4 = 0$

• Step 2: Simplify the equation.

Combine the like terms:

$(2x^2 - x^2) - 8 - 4 = 0$

This simplifies to:

$x^2 - 12 = 0$

• Step 3: Solve for $x$.

Add 12 to both sides:

$x^2 = 12$

Now take the square root of both sides:

$x = \pm \sqrt{12}$

Given the choices, the correct answer is $\pm \sqrt{12}$.

Please note that the equation can be arranged differently:

x²-16 = x +4

x² - 4² = x +4

We will first factor a trinomial for the section on the left

(x-4)(x+4) = x+4

We will then divide everything by x+4

(x-4)(x+4) / x+4 = x+4 / x+4

x-4 = 1

x = 5

To solve this problem, we'll follow these steps:

• Simplify the given expression.
• Rearrange into standard quadratic form.
• Solve using applicable method.

Let's begin the process:
1. Simplify the left-hand side: $x \cdot 3 \cdot x + 7 = 3x^2 + 7$.

2. Set up the equation by balancing: $3x^2 + 7 = 2x^2 + 9$.

3. Rearrange the terms to form a quadratic equation: $3x^2 - 2x^2 + 7 - 9 = 0$.

This simplifies to: $x^2 - 2 = 0$.

4. Solve for $x$:
By adding 2 to both sides, we have: $x^2 = 2$.
Take the square root of both sides: $x = \pm\sqrt{2}$.

Therefore, the solution to the problem is $\pm\sqrt{2}$.

To solve the equation $x^2 - 36 = 6x - 36$, follow these steps:

• Simplify the equation by subtracting 6x and 36 from both sides to get: $x^2 - 6x = 0$.
• Notice that the equation can be factored as it has a common factor: $x(x - 6) = 0$.
• According to the zero product property, set each factor equal to zero: $x = 0$ or $x - 6 = 0$.
• Solve each resulting equation: $x = 0$ and $x = 6$.

Therefore, the solutions to the quadratic equation $x^2 - 36 = 6x - 36$ are $x = 0$ or $x = 6$.