4x^2-8x-143=0

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Solution for 4x^2-8x-143=0 equation:


Simplifying
4x2 + -8x + -143 = 0

Reorder the terms:
-143 + -8x + 4x2 = 0

Solving
-143 + -8x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-35.75 + -2x + x2 = 0

Move the constant term to the right:

Add '35.75' to each side of the equation.
-35.75 + -2x + 35.75 + x2 = 0 + 35.75

Reorder the terms:
-35.75 + 35.75 + -2x + x2 = 0 + 35.75

Combine like terms: -35.75 + 35.75 = 0.00
0.00 + -2x + x2 = 0 + 35.75
-2x + x2 = 0 + 35.75

Combine like terms: 0 + 35.75 = 35.75
-2x + x2 = 35.75

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 35.75 + 1

Reorder the terms:
1 + -2x + x2 = 35.75 + 1

Combine like terms: 35.75 + 1 = 36.75
1 + -2x + x2 = 36.75

Factor a perfect square on the left side:
(x + -1)(x + -1) = 36.75

Calculate the square root of the right side: 6.062177826

Break this problem into two subproblems by setting 
(x + -1) equal to 6.062177826 and -6.062177826.

Subproblem 1

x + -1 = 6.062177826 Simplifying x + -1 = 6.062177826 Reorder the terms: -1 + x = 6.062177826 Solving -1 + x = 6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 6.062177826 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.062177826 + 1 x = 6.062177826 + 1 Combine like terms: 6.062177826 + 1 = 7.062177826 x = 7.062177826 Simplifying x = 7.062177826

Subproblem 2

x + -1 = -6.062177826 Simplifying x + -1 = -6.062177826 Reorder the terms: -1 + x = -6.062177826 Solving -1 + x = -6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -6.062177826 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.062177826 + 1 x = -6.062177826 + 1 Combine like terms: -6.062177826 + 1 = -5.062177826 x = -5.062177826 Simplifying x = -5.062177826

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.062177826, -5.062177826}

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