7x^2-10x-3=-5

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Solution for 7x^2-10x-3=-5 equation:


Simplifying
7x2 + -10x + -3 = -5

Reorder the terms:
-3 + -10x + 7x2 = -5

Solving
-3 + -10x + 7x2 = -5

Solving for variable 'x'.

Reorder the terms:
-3 + 5 + -10x + 7x2 = -5 + 5

Combine like terms: -3 + 5 = 2
2 + -10x + 7x2 = -5 + 5

Combine like terms: -5 + 5 = 0
2 + -10x + 7x2 = 0

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

Divide each side by '7'.
0.2857142857 + -1.428571429x + x2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -1.428571429x + -0.2857142857 + x2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + -1.428571429x + x2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + -1.428571429x + x2 = 0 + -0.2857142857
-1.428571429x + x2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
-1.428571429x + x2 = -0.2857142857

The x term is -1.428571429x.  Take half its coefficient (-0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
-1.428571429x + 0.5102040819 + x2 = -0.2857142857 + 0.5102040819

Reorder the terms:
0.5102040819 + -1.428571429x + x2 = -0.2857142857 + 0.5102040819

Combine like terms: -0.2857142857 + 0.5102040819 = 0.2244897962
0.5102040819 + -1.428571429x + x2 = 0.2244897962

Factor a perfect square on the left side:
(x + -0.7142857145)(x + -0.7142857145) = 0.2244897962

Calculate the square root of the right side: 0.473803542

Break this problem into two subproblems by setting 
(x + -0.7142857145) equal to 0.473803542 and -0.473803542.

Subproblem 1

x + -0.7142857145 = 0.473803542 Simplifying x + -0.7142857145 = 0.473803542 Reorder the terms: -0.7142857145 + x = 0.473803542 Solving -0.7142857145 + x = 0.473803542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 0.473803542 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 0.473803542 + 0.7142857145 x = 0.473803542 + 0.7142857145 Combine like terms: 0.473803542 + 0.7142857145 = 1.1880892565 x = 1.1880892565 Simplifying x = 1.1880892565

Subproblem 2

x + -0.7142857145 = -0.473803542 Simplifying x + -0.7142857145 = -0.473803542 Reorder the terms: -0.7142857145 + x = -0.473803542 Solving -0.7142857145 + x = -0.473803542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -0.473803542 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -0.473803542 + 0.7142857145 x = -0.473803542 + 0.7142857145 Combine like terms: -0.473803542 + 0.7142857145 = 0.2404821725 x = 0.2404821725 Simplifying x = 0.2404821725

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1880892565, 0.2404821725}

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