4.18x^2-10.89x+4.01=0

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Solution for 4.18x^2-10.89x+4.01=0 equation:


Simplifying
4.18x2 + -10.89x + 4.01 = 0

Reorder the terms:
4.01 + -10.89x + 4.18x2 = 0

Solving
4.01 + -10.89x + 4.18x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.18'.
0.9593301435 + -2.605263158x + x2 = 0

Move the constant term to the right:

Add '-0.9593301435' to each side of the equation.
0.9593301435 + -2.605263158x + -0.9593301435 + x2 = 0 + -0.9593301435

Reorder the terms:
0.9593301435 + -0.9593301435 + -2.605263158x + x2 = 0 + -0.9593301435

Combine like terms: 0.9593301435 + -0.9593301435 = 0.0000000000
0.0000000000 + -2.605263158x + x2 = 0 + -0.9593301435
-2.605263158x + x2 = 0 + -0.9593301435

Combine like terms: 0 + -0.9593301435 = -0.9593301435
-2.605263158x + x2 = -0.9593301435

The x term is -2.605263158x.  Take half its coefficient (-1.302631579).
Square it (1.696849031) and add it to both sides.

Add '1.696849031' to each side of the equation.
-2.605263158x + 1.696849031 + x2 = -0.9593301435 + 1.696849031

Reorder the terms:
1.696849031 + -2.605263158x + x2 = -0.9593301435 + 1.696849031

Combine like terms: -0.9593301435 + 1.696849031 = 0.7375188875
1.696849031 + -2.605263158x + x2 = 0.7375188875

Factor a perfect square on the left side:
(x + -1.302631579)(x + -1.302631579) = 0.7375188875

Calculate the square root of the right side: 0.858789199

Break this problem into two subproblems by setting 
(x + -1.302631579) equal to 0.858789199 and -0.858789199.

Subproblem 1

x + -1.302631579 = 0.858789199 Simplifying x + -1.302631579 = 0.858789199 Reorder the terms: -1.302631579 + x = 0.858789199 Solving -1.302631579 + x = 0.858789199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.302631579' to each side of the equation. -1.302631579 + 1.302631579 + x = 0.858789199 + 1.302631579 Combine like terms: -1.302631579 + 1.302631579 = 0.000000000 0.000000000 + x = 0.858789199 + 1.302631579 x = 0.858789199 + 1.302631579 Combine like terms: 0.858789199 + 1.302631579 = 2.161420778 x = 2.161420778 Simplifying x = 2.161420778

Subproblem 2

x + -1.302631579 = -0.858789199 Simplifying x + -1.302631579 = -0.858789199 Reorder the terms: -1.302631579 + x = -0.858789199 Solving -1.302631579 + x = -0.858789199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.302631579' to each side of the equation. -1.302631579 + 1.302631579 + x = -0.858789199 + 1.302631579 Combine like terms: -1.302631579 + 1.302631579 = 0.000000000 0.000000000 + x = -0.858789199 + 1.302631579 x = -0.858789199 + 1.302631579 Combine like terms: -0.858789199 + 1.302631579 = 0.44384238 x = 0.44384238 Simplifying x = 0.44384238

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.161420778, 0.44384238}

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