5x^2-7x-4=0

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Solution for 5x^2-7x-4=0 equation:


Simplifying
5x2 + -7x + -4 = 0

Reorder the terms:
-4 + -7x + 5x2 = 0

Solving
-4 + -7x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-0.8 + -1.4x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -1.4x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -1.4x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -1.4x + x2 = 0 + 0.8
-1.4x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-1.4x + x2 = 0.8

The x term is -1.4x.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 0.8 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 0.8 + 0.49

Combine like terms: 0.8 + 0.49 = 1.29
0.49 + -1.4x + x2 = 1.29

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 1.29

Calculate the square root of the right side: 1.135781669

Break this problem into two subproblems by setting 
(x + -0.7) equal to 1.135781669 and -1.135781669.

Subproblem 1

x + -0.7 = 1.135781669 Simplifying x + -0.7 = 1.135781669 Reorder the terms: -0.7 + x = 1.135781669 Solving -0.7 + x = 1.135781669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.135781669 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.135781669 + 0.7 x = 1.135781669 + 0.7 Combine like terms: 1.135781669 + 0.7 = 1.835781669 x = 1.835781669 Simplifying x = 1.835781669

Subproblem 2

x + -0.7 = -1.135781669 Simplifying x + -0.7 = -1.135781669 Reorder the terms: -0.7 + x = -1.135781669 Solving -0.7 + x = -1.135781669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.135781669 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.135781669 + 0.7 x = -1.135781669 + 0.7 Combine like terms: -1.135781669 + 0.7 = -0.435781669 x = -0.435781669 Simplifying x = -0.435781669

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.835781669, -0.435781669}

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