x^2+3x+4=-x^2-2x+7

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Solution for x^2+3x+4=-x^2-2x+7 equation:


Simplifying
x2 + 3x + 4 = -1x2 + -2x + 7

Reorder the terms:
4 + 3x + x2 = -1x2 + -2x + 7

Reorder the terms:
4 + 3x + x2 = 7 + -2x + -1x2

Solving
4 + 3x + x2 = 7 + -2x + -1x2

Solving for variable 'x'.

Reorder the terms:
4 + -7 + 3x + 2x + x2 + x2 = 7 + -2x + -1x2 + -7 + 2x + x2

Combine like terms: 4 + -7 = -3
-3 + 3x + 2x + x2 + x2 = 7 + -2x + -1x2 + -7 + 2x + x2

Combine like terms: 3x + 2x = 5x
-3 + 5x + x2 + x2 = 7 + -2x + -1x2 + -7 + 2x + x2

Combine like terms: x2 + x2 = 2x2
-3 + 5x + 2x2 = 7 + -2x + -1x2 + -7 + 2x + x2

Reorder the terms:
-3 + 5x + 2x2 = 7 + -7 + -2x + 2x + -1x2 + x2

Combine like terms: 7 + -7 = 0
-3 + 5x + 2x2 = 0 + -2x + 2x + -1x2 + x2
-3 + 5x + 2x2 = -2x + 2x + -1x2 + x2

Combine like terms: -2x + 2x = 0
-3 + 5x + 2x2 = 0 + -1x2 + x2
-3 + 5x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-3 + 5x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(1 + -2x) = 0

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {-3, 0.5}

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