What is the value of x?

Mathematics

1 answer:

Akimi4 [234]2 years ago

4 0

(2x + 2) = (3x + -52)

Reorder the terms:
(2 + 2x) = (3x + -52)

Remove parenthesis around (2 + 2x)
2 + 2x = (3x + -52)

Reorder the terms:
2 + 2x = (-52 + 3x)

Remove parenthesis around (-52 + 3x)
2 + 2x = -52 + 3x

Solving
2 + 2x = -52 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.
2 + 2x + -3x = -52 + 3x + -3x

Combine like terms: 2x + -3x = -1x
2 + -1x = -52 + 3x + -3x

Combine like terms: 3x + -3x = 0
2 + -1x = -52 + 0
2 + -1x = -52

Add '-2' to each side of the equation.
2 + -2 + -1x = -52 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = -52 + -2
-1x = -52 + -2

Combine like terms: -52 + -2 = -54
-1x = -54

Divide each side by '-1'.
x = 54

Simplifying
x = 54

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Answer:

$\boxed {\boxed {\sf x=2}}$

Step-by-step explanation:

The axis of symmetry can be calculated using the formula:

$x=\frac{-b}{2a}$

First we must determine a and b from the quadratic: $-x^2+4x-8$ . This is in standard form, with the highest power first in descending order.

Standard form is also: $ax^2+bx+c$

If we compare this to the quadratic given, we can conclude that:

$a= -1 \\b= 4 \\c= -8$

Substitute the values for a and b into the formula.

$x= \frac{-(4)}{2(-1)}$

Multiply in the denominator.

$x=\frac {-4}{-2}$

Divide.

$x=2$

This can also be determined from the graph. It is the x-coordinate of the vertex or the maximum/minimum. It divides the quadratic into 2 symmetrical halves.