40x^2-49x-40=0

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Solution for 40x^2-49x-40=0 equation:


Simplifying
40x2 + -49x + -40 = 0

Reorder the terms:
-40 + -49x + 40x2 = 0

Solving
-40 + -49x + 40x2 = 0

Solving for variable 'x'.

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

Divide each side by '40'.
-1 + -1.225x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.225x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.225x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.225x + x2 = 0 + 1
-1.225x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.225x + x2 = 1

The x term is -1.225x.  Take half its coefficient (-0.6125).
Square it (0.37515625) and add it to both sides.

Add '0.37515625' to each side of the equation.
-1.225x + 0.37515625 + x2 = 1 + 0.37515625

Reorder the terms:
0.37515625 + -1.225x + x2 = 1 + 0.37515625

Combine like terms: 1 + 0.37515625 = 1.37515625
0.37515625 + -1.225x + x2 = 1.37515625

Factor a perfect square on the left side:
(x + -0.6125)(x + -0.6125) = 1.37515625

Calculate the square root of the right side: 1.172670563

Break this problem into two subproblems by setting 
(x + -0.6125) equal to 1.172670563 and -1.172670563.

Subproblem 1

x + -0.6125 = 1.172670563 Simplifying x + -0.6125 = 1.172670563 Reorder the terms: -0.6125 + x = 1.172670563 Solving -0.6125 + x = 1.172670563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6125' to each side of the equation. -0.6125 + 0.6125 + x = 1.172670563 + 0.6125 Combine like terms: -0.6125 + 0.6125 = 0.0000 0.0000 + x = 1.172670563 + 0.6125 x = 1.172670563 + 0.6125 Combine like terms: 1.172670563 + 0.6125 = 1.785170563 x = 1.785170563 Simplifying x = 1.785170563

Subproblem 2

x + -0.6125 = -1.172670563 Simplifying x + -0.6125 = -1.172670563 Reorder the terms: -0.6125 + x = -1.172670563 Solving -0.6125 + x = -1.172670563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6125' to each side of the equation. -0.6125 + 0.6125 + x = -1.172670563 + 0.6125 Combine like terms: -0.6125 + 0.6125 = 0.0000 0.0000 + x = -1.172670563 + 0.6125 x = -1.172670563 + 0.6125 Combine like terms: -1.172670563 + 0.6125 = -0.560170563 x = -0.560170563 Simplifying x = -0.560170563

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.785170563, -0.560170563}

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