4x^2+19x-6=180

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Solution for 4x^2+19x-6=180 equation:


Simplifying
4x2 + 19x + -6 = 180

Reorder the terms:
-6 + 19x + 4x2 = 180

Solving
-6 + 19x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-6 + -180 + 19x + 4x2 = 180 + -180

Combine like terms: -6 + -180 = -186
-186 + 19x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-186 + 19x + 4x2 = 0

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

Divide each side by '4'.
-46.5 + 4.75x + x2 = 0

Move the constant term to the right:

Add '46.5' to each side of the equation.
-46.5 + 4.75x + 46.5 + x2 = 0 + 46.5

Reorder the terms:
-46.5 + 46.5 + 4.75x + x2 = 0 + 46.5

Combine like terms: -46.5 + 46.5 = 0.0
0.0 + 4.75x + x2 = 0 + 46.5
4.75x + x2 = 0 + 46.5

Combine like terms: 0 + 46.5 = 46.5
4.75x + x2 = 46.5

The x term is 4.75x.  Take half its coefficient (2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
4.75x + 5.640625 + x2 = 46.5 + 5.640625

Reorder the terms:
5.640625 + 4.75x + x2 = 46.5 + 5.640625

Combine like terms: 46.5 + 5.640625 = 52.140625
5.640625 + 4.75x + x2 = 52.140625

Factor a perfect square on the left side:
(x + 2.375)(x + 2.375) = 52.140625

Calculate the square root of the right side: 7.220846557

Break this problem into two subproblems by setting 
(x + 2.375) equal to 7.220846557 and -7.220846557.

Subproblem 1

x + 2.375 = 7.220846557 Simplifying x + 2.375 = 7.220846557 Reorder the terms: 2.375 + x = 7.220846557 Solving 2.375 + x = 7.220846557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 7.220846557 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 7.220846557 + -2.375 x = 7.220846557 + -2.375 Combine like terms: 7.220846557 + -2.375 = 4.845846557 x = 4.845846557 Simplifying x = 4.845846557

Subproblem 2

x + 2.375 = -7.220846557 Simplifying x + 2.375 = -7.220846557 Reorder the terms: 2.375 + x = -7.220846557 Solving 2.375 + x = -7.220846557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -7.220846557 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -7.220846557 + -2.375 x = -7.220846557 + -2.375 Combine like terms: -7.220846557 + -2.375 = -9.595846557 x = -9.595846557 Simplifying x = -9.595846557

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.845846557, -9.595846557}

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