7x^2-5x-3=0

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Solution for 7x^2-5x-3=0 equation:


Simplifying
7x2 + -5x + -3 = 0

Reorder the terms:
-3 + -5x + 7x2 = 0

Solving
-3 + -5x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-0.4285714286 + -0.7142857143x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + -0.7142857143x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + -0.7142857143x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + -0.7142857143x + x2 = 0 + 0.4285714286
-0.7142857143x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
-0.7142857143x + x2 = 0.4285714286

The x term is -0.7142857143x.  Take half its coefficient (-0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
-0.7142857143x + 0.1275510204 + x2 = 0.4285714286 + 0.1275510204

Reorder the terms:
0.1275510204 + -0.7142857143x + x2 = 0.4285714286 + 0.1275510204

Combine like terms: 0.4285714286 + 0.1275510204 = 0.556122449
0.1275510204 + -0.7142857143x + x2 = 0.556122449

Factor a perfect square on the left side:
(x + -0.3571428572)(x + -0.3571428572) = 0.556122449

Calculate the square root of the right side: 0.745736179

Break this problem into two subproblems by setting 
(x + -0.3571428572) equal to 0.745736179 and -0.745736179.

Subproblem 1

x + -0.3571428572 = 0.745736179 Simplifying x + -0.3571428572 = 0.745736179 Reorder the terms: -0.3571428572 + x = 0.745736179 Solving -0.3571428572 + x = 0.745736179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 0.745736179 + 0.3571428572 x = 0.745736179 + 0.3571428572 Combine like terms: 0.745736179 + 0.3571428572 = 1.1028790362 x = 1.1028790362 Simplifying x = 1.1028790362

Subproblem 2

x + -0.3571428572 = -0.745736179 Simplifying x + -0.3571428572 = -0.745736179 Reorder the terms: -0.3571428572 + x = -0.745736179 Solving -0.3571428572 + x = -0.745736179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -0.745736179 + 0.3571428572 x = -0.745736179 + 0.3571428572 Combine like terms: -0.745736179 + 0.3571428572 = -0.3885933218 x = -0.3885933218 Simplifying x = -0.3885933218

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1028790362, -0.3885933218}

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