0.1x^2-0.3x+2.438=150

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Solution for 0.1x^2-0.3x+2.438=150 equation:


Simplifying
0.1x2 + -0.3x + 2.438 = 150

Reorder the terms:
2.438 + -0.3x + 0.1x2 = 150

Solving
2.438 + -0.3x + 0.1x2 = 150

Solving for variable 'x'.

Reorder the terms:
2.438 + -150 + -0.3x + 0.1x2 = 150 + -150

Combine like terms: 2.438 + -150 = -147.562
-147.562 + -0.3x + 0.1x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-147.562 + -0.3x + 0.1x2 = 0

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

Divide each side by '0.1'.
-1475.62 + -3x + x2 = 0

Move the constant term to the right:

Add '1475.62' to each side of the equation.
-1475.62 + -3x + 1475.62 + x2 = 0 + 1475.62

Reorder the terms:
-1475.62 + 1475.62 + -3x + x2 = 0 + 1475.62

Combine like terms: -1475.62 + 1475.62 = 0.00
0.00 + -3x + x2 = 0 + 1475.62
-3x + x2 = 0 + 1475.62

Combine like terms: 0 + 1475.62 = 1475.62
-3x + x2 = 1475.62

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 1475.62 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1475.62 + 2.25

Combine like terms: 1475.62 + 2.25 = 1477.87
2.25 + -3x + x2 = 1477.87

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1477.87

Calculate the square root of the right side: 38.443074799

Break this problem into two subproblems by setting 
(x + -1.5) equal to 38.443074799 and -38.443074799.

Subproblem 1

x + -1.5 = 38.443074799 Simplifying x + -1.5 = 38.443074799 Reorder the terms: -1.5 + x = 38.443074799 Solving -1.5 + x = 38.443074799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 38.443074799 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 38.443074799 + 1.5 x = 38.443074799 + 1.5 Combine like terms: 38.443074799 + 1.5 = 39.943074799 x = 39.943074799 Simplifying x = 39.943074799

Subproblem 2

x + -1.5 = -38.443074799 Simplifying x + -1.5 = -38.443074799 Reorder the terms: -1.5 + x = -38.443074799 Solving -1.5 + x = -38.443074799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -38.443074799 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -38.443074799 + 1.5 x = -38.443074799 + 1.5 Combine like terms: -38.443074799 + 1.5 = -36.943074799 x = -36.943074799 Simplifying x = -36.943074799

Solution

The solution to the problem is based on the solutions from the subproblems. x = {39.943074799, -36.943074799}

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