.67(6h+3)=.33(3h-4)-h^2

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Solution for .67(6h+3)=.33(3h-4)-h^2 equation:


Simplifying
0.67(6h + 3) = 0.33(3h + -4) + -1h2

Reorder the terms:
0.67(3 + 6h) = 0.33(3h + -4) + -1h2
(3 * 0.67 + 6h * 0.67) = 0.33(3h + -4) + -1h2
(2.01 + 4.02h) = 0.33(3h + -4) + -1h2

Reorder the terms:
2.01 + 4.02h = 0.33(-4 + 3h) + -1h2
2.01 + 4.02h = (-4 * 0.33 + 3h * 0.33) + -1h2
2.01 + 4.02h = (-1.32 + 0.99h) + -1h2

Solving
2.01 + 4.02h = -1.32 + 0.99h + -1h2

Solving for variable 'h'.

Reorder the terms:
2.01 + 1.32 + 4.02h + -0.99h + h2 = -1.32 + 0.99h + -1h2 + 1.32 + -0.99h + h2

Combine like terms: 2.01 + 1.32 = 3.33
3.33 + 4.02h + -0.99h + h2 = -1.32 + 0.99h + -1h2 + 1.32 + -0.99h + h2

Combine like terms: 4.02h + -0.99h = 3.03h
3.33 + 3.03h + h2 = -1.32 + 0.99h + -1h2 + 1.32 + -0.99h + h2

Reorder the terms:
3.33 + 3.03h + h2 = -1.32 + 1.32 + 0.99h + -0.99h + -1h2 + h2

Combine like terms: -1.32 + 1.32 = 0.00
3.33 + 3.03h + h2 = 0.00 + 0.99h + -0.99h + -1h2 + h2
3.33 + 3.03h + h2 = 0.99h + -0.99h + -1h2 + h2

Combine like terms: 0.99h + -0.99h = 0.00
3.33 + 3.03h + h2 = 0.00 + -1h2 + h2
3.33 + 3.03h + h2 = -1h2 + h2

Combine like terms: -1h2 + h2 = 0
3.33 + 3.03h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3.33' to each side of the equation.
3.33 + 3.03h + -3.33 + h2 = 0 + -3.33

Reorder the terms:
3.33 + -3.33 + 3.03h + h2 = 0 + -3.33

Combine like terms: 3.33 + -3.33 = 0.00
0.00 + 3.03h + h2 = 0 + -3.33
3.03h + h2 = 0 + -3.33

Combine like terms: 0 + -3.33 = -3.33
3.03h + h2 = -3.33

The h term is 3.03h.  Take half its coefficient (1.515).
Square it (2.295225) and add it to both sides.

Add '2.295225' to each side of the equation.
3.03h + 2.295225 + h2 = -3.33 + 2.295225

Reorder the terms:
2.295225 + 3.03h + h2 = -3.33 + 2.295225

Combine like terms: -3.33 + 2.295225 = -1.034775
2.295225 + 3.03h + h2 = -1.034775

Factor a perfect square on the left side:
(h + 1.515)(h + 1.515) = -1.034775

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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