(3x^2+2x-7)+(x^2-4x+5)=0

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Solution for (3x^2+2x-7)+(x^2-4x+5)=0 equation:


Simplifying
(3x2 + 2x + -7) + (x2 + -4x + 5) = 0

Reorder the terms:
(-7 + 2x + 3x2) + (x2 + -4x + 5) = 0

Remove parenthesis around (-7 + 2x + 3x2)
-7 + 2x + 3x2 + (x2 + -4x + 5) = 0

Reorder the terms:
-7 + 2x + 3x2 + (5 + -4x + x2) = 0

Remove parenthesis around (5 + -4x + x2)
-7 + 2x + 3x2 + 5 + -4x + x2 = 0

Reorder the terms:
-7 + 5 + 2x + -4x + 3x2 + x2 = 0

Combine like terms: -7 + 5 = -2
-2 + 2x + -4x + 3x2 + x2 = 0

Combine like terms: 2x + -4x = -2x
-2 + -2x + 3x2 + x2 = 0

Combine like terms: 3x2 + x2 = 4x2
-2 + -2x + 4x2 = 0

Solving
-2 + -2x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -1x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1

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

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 = {-0.5, 1}

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