1+7x+5x^2=0

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Solution for 1+7x+5x^2=0 equation:


Simplifying
1 + 7x + 5x2 = 0

Solving
1 + 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'.
0.2 + 1.4x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.4x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.4x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.4x + x2 = 0 + -0.2
1.4x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
1.4x + x2 = -0.2

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 = -0.2 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = -0.2 + 0.49

Combine like terms: -0.2 + 0.49 = 0.29
0.49 + 1.4x + x2 = 0.29

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 0.29

Calculate the square root of the right side: 0.538516481

Break this problem into two subproblems by setting 
(x + 0.7) equal to 0.538516481 and -0.538516481.

Subproblem 1

x + 0.7 = 0.538516481 Simplifying x + 0.7 = 0.538516481 Reorder the terms: 0.7 + x = 0.538516481 Solving 0.7 + x = 0.538516481 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 = 0.538516481 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 0.538516481 + -0.7 x = 0.538516481 + -0.7 Combine like terms: 0.538516481 + -0.7 = -0.161483519 x = -0.161483519 Simplifying x = -0.161483519

Subproblem 2

x + 0.7 = -0.538516481 Simplifying x + 0.7 = -0.538516481 Reorder the terms: 0.7 + x = -0.538516481 Solving 0.7 + x = -0.538516481 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 = -0.538516481 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -0.538516481 + -0.7 x = -0.538516481 + -0.7 Combine like terms: -0.538516481 + -0.7 = -1.238516481 x = -1.238516481 Simplifying x = -1.238516481

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.161483519, -1.238516481}

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