2.65x^2-6.63x-3.98=0

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Solution for 2.65x^2-6.63x-3.98=0 equation:


Simplifying
2.65x2 + -6.63x + -3.98 = 0

Reorder the terms:
-3.98 + -6.63x + 2.65x2 = 0

Solving
-3.98 + -6.63x + 2.65x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.65'.
-1.501886792 + -2.501886792x + x2 = 0

Move the constant term to the right:

Add '1.501886792' to each side of the equation.
-1.501886792 + -2.501886792x + 1.501886792 + x2 = 0 + 1.501886792

Reorder the terms:
-1.501886792 + 1.501886792 + -2.501886792x + x2 = 0 + 1.501886792

Combine like terms: -1.501886792 + 1.501886792 = 0.000000000
0.000000000 + -2.501886792x + x2 = 0 + 1.501886792
-2.501886792x + x2 = 0 + 1.501886792

Combine like terms: 0 + 1.501886792 = 1.501886792
-2.501886792x + x2 = 1.501886792

The x term is -2.501886792x.  Take half its coefficient (-1.250943396).
Square it (1.564859380) and add it to both sides.

Add '1.564859380' to each side of the equation.
-2.501886792x + 1.564859380 + x2 = 1.501886792 + 1.564859380

Reorder the terms:
1.564859380 + -2.501886792x + x2 = 1.501886792 + 1.564859380

Combine like terms: 1.501886792 + 1.564859380 = 3.066746172
1.564859380 + -2.501886792x + x2 = 3.066746172

Factor a perfect square on the left side:
(x + -1.250943396)(x + -1.250943396) = 3.066746172

Calculate the square root of the right side: 1.751212772

Break this problem into two subproblems by setting 
(x + -1.250943396) equal to 1.751212772 and -1.751212772.

Subproblem 1

x + -1.250943396 = 1.751212772 Simplifying x + -1.250943396 = 1.751212772 Reorder the terms: -1.250943396 + x = 1.751212772 Solving -1.250943396 + x = 1.751212772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.250943396' to each side of the equation. -1.250943396 + 1.250943396 + x = 1.751212772 + 1.250943396 Combine like terms: -1.250943396 + 1.250943396 = 0.000000000 0.000000000 + x = 1.751212772 + 1.250943396 x = 1.751212772 + 1.250943396 Combine like terms: 1.751212772 + 1.250943396 = 3.002156168 x = 3.002156168 Simplifying x = 3.002156168

Subproblem 2

x + -1.250943396 = -1.751212772 Simplifying x + -1.250943396 = -1.751212772 Reorder the terms: -1.250943396 + x = -1.751212772 Solving -1.250943396 + x = -1.751212772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.250943396' to each side of the equation. -1.250943396 + 1.250943396 + x = -1.751212772 + 1.250943396 Combine like terms: -1.250943396 + 1.250943396 = 0.000000000 0.000000000 + x = -1.751212772 + 1.250943396 x = -1.751212772 + 1.250943396 Combine like terms: -1.751212772 + 1.250943396 = -0.500269376 x = -0.500269376 Simplifying x = -0.500269376

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.002156168, -0.500269376}

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