f(3)+f(-3)=-x^2-4x+5

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Solution for f(3)+f(-3)=-x^2-4x+5 equation:


Simplifying
f(3) + f(-3) = -1x2 + -4x + 5

Reorder the terms for easier multiplication:
3f + f(-3) = -1x2 + -4x + 5

Reorder the terms for easier multiplication:
3f + -3f = -1x2 + -4x + 5

Combine like terms: 3f + -3f = 0
0 = -1x2 + -4x + 5

Reorder the terms:
0 = 5 + -4x + -1x2

Solving
0 = 5 + -4x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + 4x + x2 = 5 + -4x + -1x2 + -5 + 4x + x2

Reorder the terms:
-5 + 4x + x2 = 5 + -5 + -4x + 4x + -1x2 + x2

Combine like terms: 5 + -5 = 0
-5 + 4x + x2 = 0 + -4x + 4x + -1x2 + x2
-5 + 4x + x2 = -4x + 4x + -1x2 + x2

Combine like terms: -4x + 4x = 0
-5 + 4x + x2 = 0 + -1x2 + x2
-5 + 4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-5 + 4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {-5, 1}

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