(w^2-4w+7)+(3w^2+5w-3)=

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


Simplifying
(w2 + -4w + 7) + (3w2 + 5w + -3) = 0

Reorder the terms:
(7 + -4w + w2) + (3w2 + 5w + -3) = 0

Remove parenthesis around (7 + -4w + w2)
7 + -4w + w2 + (3w2 + 5w + -3) = 0

Reorder the terms:
7 + -4w + w2 + (-3 + 5w + 3w2) = 0

Remove parenthesis around (-3 + 5w + 3w2)
7 + -4w + w2 + -3 + 5w + 3w2 = 0

Reorder the terms:
7 + -3 + -4w + 5w + w2 + 3w2 = 0

Combine like terms: 7 + -3 = 4
4 + -4w + 5w + w2 + 3w2 = 0

Combine like terms: -4w + 5w = 1w
4 + 1w + w2 + 3w2 = 0

Combine like terms: w2 + 3w2 = 4w2
4 + 1w + 4w2 = 0

Solving
4 + 1w + 4w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
1 + 0.25w + w2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.25w + -1 + w2 = 0 + -1

Reorder the terms:
1 + -1 + 0.25w + w2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.25w + w2 = 0 + -1
0.25w + w2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.25w + w2 = -1

The w term is 0.25w.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25w + 0.015625 + w2 = -1 + 0.015625

Reorder the terms:
0.015625 + 0.25w + w2 = -1 + 0.015625

Combine like terms: -1 + 0.015625 = -0.984375
0.015625 + 0.25w + w2 = -0.984375

Factor a perfect square on the left side:
(w + 0.125)(w + 0.125) = -0.984375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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