2x^2+6x-71=0

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Solution for 2x^2+6x-71=0 equation:


Simplifying
2x2 + 6x + -71 = 0

Reorder the terms:
-71 + 6x + 2x2 = 0

Solving
-71 + 6x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-35.5 + 3x + x2 = 0

Move the constant term to the right:

Add '35.5' to each side of the equation.
-35.5 + 3x + 35.5 + x2 = 0 + 35.5

Reorder the terms:
-35.5 + 35.5 + 3x + x2 = 0 + 35.5

Combine like terms: -35.5 + 35.5 = 0.0
0.0 + 3x + x2 = 0 + 35.5
3x + x2 = 0 + 35.5

Combine like terms: 0 + 35.5 = 35.5
3x + x2 = 35.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 35.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 35.5 + 2.25

Combine like terms: 35.5 + 2.25 = 37.75
2.25 + 3x + x2 = 37.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 37.75

Calculate the square root of the right side: 6.144102864

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.144102864 and -6.144102864.

Subproblem 1

x + 1.5 = 6.144102864 Simplifying x + 1.5 = 6.144102864 Reorder the terms: 1.5 + x = 6.144102864 Solving 1.5 + x = 6.144102864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 6.144102864 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.144102864 + -1.5 x = 6.144102864 + -1.5 Combine like terms: 6.144102864 + -1.5 = 4.644102864 x = 4.644102864 Simplifying x = 4.644102864

Subproblem 2

x + 1.5 = -6.144102864 Simplifying x + 1.5 = -6.144102864 Reorder the terms: 1.5 + x = -6.144102864 Solving 1.5 + x = -6.144102864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -6.144102864 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.144102864 + -1.5 x = -6.144102864 + -1.5 Combine like terms: -6.144102864 + -1.5 = -7.644102864 x = -7.644102864 Simplifying x = -7.644102864

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.644102864, -7.644102864}

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