5x^2+14x-49=0

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Solution for 5x^2+14x-49=0 equation:


Simplifying
5x2 + 14x + -49 = 0

Reorder the terms:
-49 + 14x + 5x2 = 0

Solving
-49 + 14x + 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'.
-9.8 + 2.8x + x2 = 0

Move the constant term to the right:

Add '9.8' to each side of the equation.
-9.8 + 2.8x + 9.8 + x2 = 0 + 9.8

Reorder the terms:
-9.8 + 9.8 + 2.8x + x2 = 0 + 9.8

Combine like terms: -9.8 + 9.8 = 0.0
0.0 + 2.8x + x2 = 0 + 9.8
2.8x + x2 = 0 + 9.8

Combine like terms: 0 + 9.8 = 9.8
2.8x + x2 = 9.8

The x term is 2.8x.  Take half its coefficient (1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
2.8x + 1.96 + x2 = 9.8 + 1.96

Reorder the terms:
1.96 + 2.8x + x2 = 9.8 + 1.96

Combine like terms: 9.8 + 1.96 = 11.76
1.96 + 2.8x + x2 = 11.76

Factor a perfect square on the left side:
(x + 1.4)(x + 1.4) = 11.76

Calculate the square root of the right side: 3.42928564

Break this problem into two subproblems by setting 
(x + 1.4) equal to 3.42928564 and -3.42928564.

Subproblem 1

x + 1.4 = 3.42928564 Simplifying x + 1.4 = 3.42928564 Reorder the terms: 1.4 + x = 3.42928564 Solving 1.4 + x = 3.42928564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 3.42928564 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 3.42928564 + -1.4 x = 3.42928564 + -1.4 Combine like terms: 3.42928564 + -1.4 = 2.02928564 x = 2.02928564 Simplifying x = 2.02928564

Subproblem 2

x + 1.4 = -3.42928564 Simplifying x + 1.4 = -3.42928564 Reorder the terms: 1.4 + x = -3.42928564 Solving 1.4 + x = -3.42928564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -3.42928564 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -3.42928564 + -1.4 x = -3.42928564 + -1.4 Combine like terms: -3.42928564 + -1.4 = -4.82928564 x = -4.82928564 Simplifying x = -4.82928564

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.02928564, -4.82928564}

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