-4.9x^2+27x+2.4=0

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Solution for -4.9x^2+27x+2.4=0 equation:


Simplifying
-4.9x2 + 27x + 2.4 = 0

Reorder the terms:
2.4 + 27x + -4.9x2 = 0

Solving
2.4 + 27x + -4.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-0.4897959184 + -5.510204082x + x2 = 0

Move the constant term to the right:

Add '0.4897959184' to each side of the equation.
-0.4897959184 + -5.510204082x + 0.4897959184 + x2 = 0 + 0.4897959184

Reorder the terms:
-0.4897959184 + 0.4897959184 + -5.510204082x + x2 = 0 + 0.4897959184

Combine like terms: -0.4897959184 + 0.4897959184 = 0.0000000000
0.0000000000 + -5.510204082x + x2 = 0 + 0.4897959184
-5.510204082x + x2 = 0 + 0.4897959184

Combine like terms: 0 + 0.4897959184 = 0.4897959184
-5.510204082x + x2 = 0.4897959184

The x term is -5.510204082x.  Take half its coefficient (-2.755102041).
Square it (7.590587256) and add it to both sides.

Add '7.590587256' to each side of the equation.
-5.510204082x + 7.590587256 + x2 = 0.4897959184 + 7.590587256

Reorder the terms:
7.590587256 + -5.510204082x + x2 = 0.4897959184 + 7.590587256

Combine like terms: 0.4897959184 + 7.590587256 = 8.0803831744
7.590587256 + -5.510204082x + x2 = 8.0803831744

Factor a perfect square on the left side:
(x + -2.755102041)(x + -2.755102041) = 8.0803831744

Calculate the square root of the right side: 2.84260148

Break this problem into two subproblems by setting 
(x + -2.755102041) equal to 2.84260148 and -2.84260148.

Subproblem 1

x + -2.755102041 = 2.84260148 Simplifying x + -2.755102041 = 2.84260148 Reorder the terms: -2.755102041 + x = 2.84260148 Solving -2.755102041 + x = 2.84260148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.755102041' to each side of the equation. -2.755102041 + 2.755102041 + x = 2.84260148 + 2.755102041 Combine like terms: -2.755102041 + 2.755102041 = 0.000000000 0.000000000 + x = 2.84260148 + 2.755102041 x = 2.84260148 + 2.755102041 Combine like terms: 2.84260148 + 2.755102041 = 5.597703521 x = 5.597703521 Simplifying x = 5.597703521

Subproblem 2

x + -2.755102041 = -2.84260148 Simplifying x + -2.755102041 = -2.84260148 Reorder the terms: -2.755102041 + x = -2.84260148 Solving -2.755102041 + x = -2.84260148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.755102041' to each side of the equation. -2.755102041 + 2.755102041 + x = -2.84260148 + 2.755102041 Combine like terms: -2.755102041 + 2.755102041 = 0.000000000 0.000000000 + x = -2.84260148 + 2.755102041 x = -2.84260148 + 2.755102041 Combine like terms: -2.84260148 + 2.755102041 = -0.087499439 x = -0.087499439 Simplifying x = -0.087499439

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.597703521, -0.087499439}

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