x^2-4.5x+2.9=0

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Solution for x^2-4.5x+2.9=0 equation:


Simplifying
x2 + -4.5x + 2.9 = 0

Reorder the terms:
2.9 + -4.5x + x2 = 0

Solving
2.9 + -4.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.9' to each side of the equation.
2.9 + -4.5x + -2.9 + x2 = 0 + -2.9

Reorder the terms:
2.9 + -2.9 + -4.5x + x2 = 0 + -2.9

Combine like terms: 2.9 + -2.9 = 0.0
0.0 + -4.5x + x2 = 0 + -2.9
-4.5x + x2 = 0 + -2.9

Combine like terms: 0 + -2.9 = -2.9
-4.5x + x2 = -2.9

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = -2.9 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = -2.9 + 5.0625

Combine like terms: -2.9 + 5.0625 = 2.1625
5.0625 + -4.5x + x2 = 2.1625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 2.1625

Calculate the square root of the right side: 1.470544117

Break this problem into two subproblems by setting 
(x + -2.25) equal to 1.470544117 and -1.470544117.

Subproblem 1

x + -2.25 = 1.470544117 Simplifying x + -2.25 = 1.470544117 Reorder the terms: -2.25 + x = 1.470544117 Solving -2.25 + x = 1.470544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.470544117 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.470544117 + 2.25 x = 1.470544117 + 2.25 Combine like terms: 1.470544117 + 2.25 = 3.720544117 x = 3.720544117 Simplifying x = 3.720544117

Subproblem 2

x + -2.25 = -1.470544117 Simplifying x + -2.25 = -1.470544117 Reorder the terms: -2.25 + x = -1.470544117 Solving -2.25 + x = -1.470544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.470544117 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.470544117 + 2.25 x = -1.470544117 + 2.25 Combine like terms: -1.470544117 + 2.25 = 0.779455883 x = 0.779455883 Simplifying x = 0.779455883

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.720544117, 0.779455883}

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