.45x^2-2.61x+2.88=0

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Solution for .45x^2-2.61x+2.88=0 equation:


Simplifying
0.45x2 + -2.61x + 2.88 = 0

Reorder the terms:
2.88 + -2.61x + 0.45x2 = 0

Solving
2.88 + -2.61x + 0.45x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.45'.
6.4 + -5.8x + x2 = 0

Move the constant term to the right:

Add '-6.4' to each side of the equation.
6.4 + -5.8x + -6.4 + x2 = 0 + -6.4

Reorder the terms:
6.4 + -6.4 + -5.8x + x2 = 0 + -6.4

Combine like terms: 6.4 + -6.4 = 0.0
0.0 + -5.8x + x2 = 0 + -6.4
-5.8x + x2 = 0 + -6.4

Combine like terms: 0 + -6.4 = -6.4
-5.8x + x2 = -6.4

The x term is -5.8x.  Take half its coefficient (-2.9).
Square it (8.41) and add it to both sides.

Add '8.41' to each side of the equation.
-5.8x + 8.41 + x2 = -6.4 + 8.41

Reorder the terms:
8.41 + -5.8x + x2 = -6.4 + 8.41

Combine like terms: -6.4 + 8.41 = 2.01
8.41 + -5.8x + x2 = 2.01

Factor a perfect square on the left side:
(x + -2.9)(x + -2.9) = 2.01

Calculate the square root of the right side: 1.417744688

Break this problem into two subproblems by setting 
(x + -2.9) equal to 1.417744688 and -1.417744688.

Subproblem 1

x + -2.9 = 1.417744688 Simplifying x + -2.9 = 1.417744688 Reorder the terms: -2.9 + x = 1.417744688 Solving -2.9 + x = 1.417744688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = 1.417744688 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = 1.417744688 + 2.9 x = 1.417744688 + 2.9 Combine like terms: 1.417744688 + 2.9 = 4.317744688 x = 4.317744688 Simplifying x = 4.317744688

Subproblem 2

x + -2.9 = -1.417744688 Simplifying x + -2.9 = -1.417744688 Reorder the terms: -2.9 + x = -1.417744688 Solving -2.9 + x = -1.417744688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = -1.417744688 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = -1.417744688 + 2.9 x = -1.417744688 + 2.9 Combine like terms: -1.417744688 + 2.9 = 1.482255312 x = 1.482255312 Simplifying x = 1.482255312

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.317744688, 1.482255312}

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