4.01x^2-9.66x+3.06=0

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Solution for 4.01x^2-9.66x+3.06=0 equation:


Simplifying
4.01x2 + -9.66x + 3.06 = 0

Reorder the terms:
3.06 + -9.66x + 4.01x2 = 0

Solving
3.06 + -9.66x + 4.01x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.01'.
0.7630922693 + -2.408977556x + x2 = 0

Move the constant term to the right:

Add '-0.7630922693' to each side of the equation.
0.7630922693 + -2.408977556x + -0.7630922693 + x2 = 0 + -0.7630922693

Reorder the terms:
0.7630922693 + -0.7630922693 + -2.408977556x + x2 = 0 + -0.7630922693

Combine like terms: 0.7630922693 + -0.7630922693 = 0.0000000000
0.0000000000 + -2.408977556x + x2 = 0 + -0.7630922693
-2.408977556x + x2 = 0 + -0.7630922693

Combine like terms: 0 + -0.7630922693 = -0.7630922693
-2.408977556x + x2 = -0.7630922693

The x term is -2.408977556x.  Take half its coefficient (-1.204488778).
Square it (1.450793216) and add it to both sides.

Add '1.450793216' to each side of the equation.
-2.408977556x + 1.450793216 + x2 = -0.7630922693 + 1.450793216

Reorder the terms:
1.450793216 + -2.408977556x + x2 = -0.7630922693 + 1.450793216

Combine like terms: -0.7630922693 + 1.450793216 = 0.6877009467
1.450793216 + -2.408977556x + x2 = 0.6877009467

Factor a perfect square on the left side:
(x + -1.204488778)(x + -1.204488778) = 0.6877009467

Calculate the square root of the right side: 0.829277364

Break this problem into two subproblems by setting 
(x + -1.204488778) equal to 0.829277364 and -0.829277364.

Subproblem 1

x + -1.204488778 = 0.829277364 Simplifying x + -1.204488778 = 0.829277364 Reorder the terms: -1.204488778 + x = 0.829277364 Solving -1.204488778 + x = 0.829277364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.204488778' to each side of the equation. -1.204488778 + 1.204488778 + x = 0.829277364 + 1.204488778 Combine like terms: -1.204488778 + 1.204488778 = 0.000000000 0.000000000 + x = 0.829277364 + 1.204488778 x = 0.829277364 + 1.204488778 Combine like terms: 0.829277364 + 1.204488778 = 2.033766142 x = 2.033766142 Simplifying x = 2.033766142

Subproblem 2

x + -1.204488778 = -0.829277364 Simplifying x + -1.204488778 = -0.829277364 Reorder the terms: -1.204488778 + x = -0.829277364 Solving -1.204488778 + x = -0.829277364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.204488778' to each side of the equation. -1.204488778 + 1.204488778 + x = -0.829277364 + 1.204488778 Combine like terms: -1.204488778 + 1.204488778 = 0.000000000 0.000000000 + x = -0.829277364 + 1.204488778 x = -0.829277364 + 1.204488778 Combine like terms: -0.829277364 + 1.204488778 = 0.375211414 x = 0.375211414 Simplifying x = 0.375211414

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.033766142, 0.375211414}

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