7x^2+23x-4=0

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Solution for 7x^2+23x-4=0 equation:


Simplifying
7x2 + 23x + -4 = 0

Reorder the terms:
-4 + 23x + 7x2 = 0

Solving
-4 + 23x + 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'.
-0.5714285714 + 3.285714286x + x2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 3.285714286x + 0.5714285714 + x2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 3.285714286x + x2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 3.285714286x + x2 = 0 + 0.5714285714
3.285714286x + x2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
3.285714286x + x2 = 0.5714285714

The x term is 3.285714286x.  Take half its coefficient (1.642857143).
Square it (2.698979592) and add it to both sides.

Add '2.698979592' to each side of the equation.
3.285714286x + 2.698979592 + x2 = 0.5714285714 + 2.698979592

Reorder the terms:
2.698979592 + 3.285714286x + x2 = 0.5714285714 + 2.698979592

Combine like terms: 0.5714285714 + 2.698979592 = 3.2704081634
2.698979592 + 3.285714286x + x2 = 3.2704081634

Factor a perfect square on the left side:
(x + 1.642857143)(x + 1.642857143) = 3.2704081634

Calculate the square root of the right side: 1.808426986

Break this problem into two subproblems by setting 
(x + 1.642857143) equal to 1.808426986 and -1.808426986.

Subproblem 1

x + 1.642857143 = 1.808426986 Simplifying x + 1.642857143 = 1.808426986 Reorder the terms: 1.642857143 + x = 1.808426986 Solving 1.642857143 + x = 1.808426986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x = 1.808426986 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = 1.808426986 + -1.642857143 x = 1.808426986 + -1.642857143 Combine like terms: 1.808426986 + -1.642857143 = 0.165569843 x = 0.165569843 Simplifying x = 0.165569843

Subproblem 2

x + 1.642857143 = -1.808426986 Simplifying x + 1.642857143 = -1.808426986 Reorder the terms: 1.642857143 + x = -1.808426986 Solving 1.642857143 + x = -1.808426986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x = -1.808426986 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = -1.808426986 + -1.642857143 x = -1.808426986 + -1.642857143 Combine like terms: -1.808426986 + -1.642857143 = -3.451284129 x = -3.451284129 Simplifying x = -3.451284129

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.165569843, -3.451284129}

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