7x^2+20x-18=0

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Solution for 7x^2+20x-18=0 equation:


Simplifying
7x2 + 20x + -18 = 0

Reorder the terms:
-18 + 20x + 7x2 = 0

Solving
-18 + 20x + 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'.
-2.571428571 + 2.857142857x + x2 = 0

Move the constant term to the right:

Add '2.571428571' to each side of the equation.
-2.571428571 + 2.857142857x + 2.571428571 + x2 = 0 + 2.571428571

Reorder the terms:
-2.571428571 + 2.571428571 + 2.857142857x + x2 = 0 + 2.571428571

Combine like terms: -2.571428571 + 2.571428571 = 0.000000000
0.000000000 + 2.857142857x + x2 = 0 + 2.571428571
2.857142857x + x2 = 0 + 2.571428571

Combine like terms: 0 + 2.571428571 = 2.571428571
2.857142857x + x2 = 2.571428571

The x term is 2.857142857x.  Take half its coefficient (1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
2.857142857x + 2.040816328 + x2 = 2.571428571 + 2.040816328

Reorder the terms:
2.040816328 + 2.857142857x + x2 = 2.571428571 + 2.040816328

Combine like terms: 2.571428571 + 2.040816328 = 4.612244899
2.040816328 + 2.857142857x + x2 = 4.612244899

Factor a perfect square on the left side:
(x + 1.428571429)(x + 1.428571429) = 4.612244899

Calculate the square root of the right side: 2.147613769

Break this problem into two subproblems by setting 
(x + 1.428571429) equal to 2.147613769 and -2.147613769.

Subproblem 1

x + 1.428571429 = 2.147613769 Simplifying x + 1.428571429 = 2.147613769 Reorder the terms: 1.428571429 + x = 2.147613769 Solving 1.428571429 + x = 2.147613769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = 2.147613769 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = 2.147613769 + -1.428571429 x = 2.147613769 + -1.428571429 Combine like terms: 2.147613769 + -1.428571429 = 0.71904234 x = 0.71904234 Simplifying x = 0.71904234

Subproblem 2

x + 1.428571429 = -2.147613769 Simplifying x + 1.428571429 = -2.147613769 Reorder the terms: 1.428571429 + x = -2.147613769 Solving 1.428571429 + x = -2.147613769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = -2.147613769 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = -2.147613769 + -1.428571429 x = -2.147613769 + -1.428571429 Combine like terms: -2.147613769 + -1.428571429 = -3.576185198 x = -3.576185198 Simplifying x = -3.576185198

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.71904234, -3.576185198}

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