0=2.43x^2-6.08x-3.65

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Solution for 0=2.43x^2-6.08x-3.65 equation:


Simplifying
0 = 2.43x2 + -6.08x + -3.65

Reorder the terms:
0 = -3.65 + -6.08x + 2.43x2

Solving
0 = -3.65 + -6.08x + 2.43x2

Solving for variable 'x'.

Combine like terms: 0 + 3.65 = 3.65
3.65 + 6.08x + -2.43x2 = -3.65 + -6.08x + 2.43x2 + 3.65 + 6.08x + -2.43x2

Reorder the terms:
3.65 + 6.08x + -2.43x2 = -3.65 + 3.65 + -6.08x + 6.08x + 2.43x2 + -2.43x2

Combine like terms: -3.65 + 3.65 = 0.00
3.65 + 6.08x + -2.43x2 = 0.00 + -6.08x + 6.08x + 2.43x2 + -2.43x2
3.65 + 6.08x + -2.43x2 = -6.08x + 6.08x + 2.43x2 + -2.43x2

Combine like terms: -6.08x + 6.08x = 0.00
3.65 + 6.08x + -2.43x2 = 0.00 + 2.43x2 + -2.43x2
3.65 + 6.08x + -2.43x2 = 2.43x2 + -2.43x2

Combine like terms: 2.43x2 + -2.43x2 = 0.00
3.65 + 6.08x + -2.43x2 = 0.00

Begin completing the square.  Divide all terms by
-2.43 the coefficient of the squared term: 

Divide each side by '-2.43'.
-1.502057613 + -2.502057613x + x2 = 0

Move the constant term to the right:

Add '1.502057613' to each side of the equation.
-1.502057613 + -2.502057613x + 1.502057613 + x2 = 0 + 1.502057613

Reorder the terms:
-1.502057613 + 1.502057613 + -2.502057613x + x2 = 0 + 1.502057613

Combine like terms: -1.502057613 + 1.502057613 = 0.000000000
0.000000000 + -2.502057613x + x2 = 0 + 1.502057613
-2.502057613x + x2 = 0 + 1.502057613

Combine like terms: 0 + 1.502057613 = 1.502057613
-2.502057613x + x2 = 1.502057613

The x term is -2.502057613x.  Take half its coefficient (-1.251028807).
Square it (1.565073076) and add it to both sides.

Add '1.565073076' to each side of the equation.
-2.502057613x + 1.565073076 + x2 = 1.502057613 + 1.565073076

Reorder the terms:
1.565073076 + -2.502057613x + x2 = 1.502057613 + 1.565073076

Combine like terms: 1.502057613 + 1.565073076 = 3.067130689
1.565073076 + -2.502057613x + x2 = 3.067130689

Factor a perfect square on the left side:
(x + -1.251028807)(x + -1.251028807) = 3.067130689

Calculate the square root of the right side: 1.751322554

Break this problem into two subproblems by setting 
(x + -1.251028807) equal to 1.751322554 and -1.751322554.

Subproblem 1

x + -1.251028807 = 1.751322554 Simplifying x + -1.251028807 = 1.751322554 Reorder the terms: -1.251028807 + x = 1.751322554 Solving -1.251028807 + x = 1.751322554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.251028807' to each side of the equation. -1.251028807 + 1.251028807 + x = 1.751322554 + 1.251028807 Combine like terms: -1.251028807 + 1.251028807 = 0.000000000 0.000000000 + x = 1.751322554 + 1.251028807 x = 1.751322554 + 1.251028807 Combine like terms: 1.751322554 + 1.251028807 = 3.002351361 x = 3.002351361 Simplifying x = 3.002351361

Subproblem 2

x + -1.251028807 = -1.751322554 Simplifying x + -1.251028807 = -1.751322554 Reorder the terms: -1.251028807 + x = -1.751322554 Solving -1.251028807 + x = -1.751322554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.251028807' to each side of the equation. -1.251028807 + 1.251028807 + x = -1.751322554 + 1.251028807 Combine like terms: -1.251028807 + 1.251028807 = 0.000000000 0.000000000 + x = -1.751322554 + 1.251028807 x = -1.751322554 + 1.251028807 Combine like terms: -1.751322554 + 1.251028807 = -0.500293747 x = -0.500293747 Simplifying x = -0.500293747

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.002351361, -0.500293747}

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