-4(x*4x)= 2(2-x)+10
Let's simplify the equation step by step.
-4(x*4x) = 2(2-x) + 10
First, we can simplify the left side by multiplying x and 4x:
-4(4x^2) = 2(2-x) + 10
Next, we can simplify the right side by distributing 2 to both terms inside the parentheses:
-4(4x^2) = 4 - 2x + 10
Now, we can combine like terms on the right side:
-4(4x^2) = 14 - 2x
To simplify the left side, we can multiply -4 by 4x^2:
-16x^2 = 14 - 2x
Now, let's move all terms to one side of the equation:
-16x^2 + 2x - 14 = 0
This is a quadratic equation. To solve it, we can factor or use the quadratic formula. However, in this case, factoring may be difficult. Therefore, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For this equation, a = -16, b = 2, and c = -14. Substituting these values into the quadratic formula:
x = (-2 ± √(2^2 - 4(-16)(-14))) / (2*-16)
Simplifying this further:
x = (-2 ± √(4 - 896)) / -32
x = (-2 ± √(-892)) / -32
Since the square root of a negative number is not a real number, there are no real solutions for this equation.
To solve the given equation, let's start by simplifying each side of the equation step-by-step.
1. Distribute -4 to both terms inside the parentheses on the left side:
-4 * (x * 4x) = -4 * (4x^2) = -16x^2
2. Distribute 2 to both terms inside the parentheses on the right side:
2 * (2 - x) = 2*2 - 2*x = 4 - 2x
After simplifying, the equation becomes:
-16x^2 = 4 - 2x + 10
Now, let's combine like terms on the right side:
-16x^2 = 14 - 2x
To continue, let's rearrange the equation by moving all terms to one side:
-16x^2 + 2x -14 = 0
Now, we have a quadratic equation. Let's solve it by factoring or using the quadratic formula:
Unfortunately, the given equation cannot be easily factored. So, we will use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case:
a = -16
b = 2
c = -14
Substituting these values into the quadratic formula:
x = (-2 ± √(2^2 - 4(-16)(-14))) / (2(-16))
Simplifying:
x = (-2 ± √(4 - 896)) / (-32)
x = (-2 ± √(-892)) / (-32)
As the value inside the square root is negative, the equation has no real solutions. Therefore, the original equation -4(x*4x) = 2(2-x) + 10 has no real solutions.
To solve this equation, we need to simplify and re-arrange the terms. Let's break it down step by step:
Step 1: Multiply the numbers within the parentheses on both sides of the equation.
-4(x*4x) becomes -4(4x^2), which simplifies to -16x^2.
2(2-x) becomes 4 - 2x.
The equation now becomes:
-16x^2 = 4 - 2x + 10
Step 2: Combine like terms on the right-hand side of the equation.
4 and 10 can be combined to give 14.
The equation now becomes:
-16x^2 = 14 - 2x
Step 3: Move all terms to one side to set the equation to zero.
The equation is now:
-16x^2 + 2x - 14 = 0
Step 4: To find the solution, we can either factor, complete the square, or use the quadratic formula. In this case, let's use the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation: -16x^2 + 2x - 14 = 0, the values of a, b, and c are:
a = -16, b = 2, c = -14
Plugging these values into the quadratic formula, we get:
x = (-2 ± √(2^2 - 4(-16)(-14))) / (2(-16))
Step 5: Simplify the equation further.
x = (-2 ± √(4 - 896)) / (-32)
x = (-2 ± √(-892)) / (-32)
At this point, we have a negative number under the square root, which means there are no real solutions to this equation. The solution to the equation is imaginary.