4x^2+19x-45=0

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Solution for 4x^2+19x-45=0 equation:


Simplifying
4x2 + 19x + -45 = 0

Reorder the terms:
-45 + 19x + 4x2 = 0

Solving
-45 + 19x + 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'.
-11.25 + 4.75x + x2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + 4.75x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + 4.75x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + 4.75x + x2 = 0 + 11.25
4.75x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
4.75x + x2 = 11.25

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 = 11.25 + 5.640625

Reorder the terms:
5.640625 + 4.75x + x2 = 11.25 + 5.640625

Combine like terms: 11.25 + 5.640625 = 16.890625
5.640625 + 4.75x + x2 = 16.890625

Factor a perfect square on the left side:
(x + 2.375)(x + 2.375) = 16.890625

Calculate the square root of the right side: 4.109820556

Break this problem into two subproblems by setting 
(x + 2.375) equal to 4.109820556 and -4.109820556.

Subproblem 1

x + 2.375 = 4.109820556 Simplifying x + 2.375 = 4.109820556 Reorder the terms: 2.375 + x = 4.109820556 Solving 2.375 + x = 4.109820556 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 = 4.109820556 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 4.109820556 + -2.375 x = 4.109820556 + -2.375 Combine like terms: 4.109820556 + -2.375 = 1.734820556 x = 1.734820556 Simplifying x = 1.734820556

Subproblem 2

x + 2.375 = -4.109820556 Simplifying x + 2.375 = -4.109820556 Reorder the terms: 2.375 + x = -4.109820556 Solving 2.375 + x = -4.109820556 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 = -4.109820556 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -4.109820556 + -2.375 x = -4.109820556 + -2.375 Combine like terms: -4.109820556 + -2.375 = -6.484820556 x = -6.484820556 Simplifying x = -6.484820556

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.734820556, -6.484820556}

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