4.9x^2+2.74x-10=0

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Solution for 4.9x^2+2.74x-10=0 equation: 


Simplifying
4.9x2 + 2.74x + -10 = 0

Reorder the terms:
-10 + 2.74x + 4.9x2 = 0

Solving
-10 + 2.74x + 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'.
-2.040816327 + 0.5591836735x + x2 = 0

Move the constant term to the right:

Add '2.040816327' to each side of the equation.
-2.040816327 + 0.5591836735x + 2.040816327 + x2 = 0 + 2.040816327

Reorder the terms:
-2.040816327 + 2.040816327 + 0.5591836735x + x2 = 0 + 2.040816327

Combine like terms: -2.040816327 + 2.040816327 = 0.000000000
0.000000000 + 0.5591836735x + x2 = 0 + 2.040816327
0.5591836735x + x2 = 0 + 2.040816327

Combine like terms: 0 + 2.040816327 = 2.040816327
0.5591836735x + x2 = 2.040816327

The x term is 0.5591836735x.  Take half its coefficient (0.2795918368).
Square it (0.07817159521) and add it to both sides.

Add '0.07817159521' to each side of the equation.
0.5591836735x + 0.07817159521 + x2 = 2.040816327 + 0.07817159521

Reorder the terms:
0.07817159521 + 0.5591836735x + x2 = 2.040816327 + 0.07817159521

Combine like terms: 2.040816327 + 0.07817159521 = 2.11898792221
0.07817159521 + 0.5591836735x + x2 = 2.11898792221

Factor a perfect square on the left side:
(x + 0.2795918368)(x + 0.2795918368) = 2.11898792221

Calculate the square root of the right side: 1.455674387

Break this problem into two subproblems by setting 
(x + 0.2795918368) equal to 1.455674387 and -1.455674387.


Subproblem 1
x + 0.2795918368 = 1.455674387

Simplifying
x + 0.2795918368 = 1.455674387

Reorder the terms:
0.2795918368 + x = 1.455674387

Solving
0.2795918368 + x = 1.455674387

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2795918368' to each side of the equation.
0.2795918368 + -0.2795918368 + x = 1.455674387 + -0.2795918368

Combine like terms: 0.2795918368 + -0.2795918368 = 0.0000000000
0.0000000000 + x = 1.455674387 + -0.2795918368
x = 1.455674387 + -0.2795918368

Combine like terms: 1.455674387 + -0.2795918368 = 1.1760825502
x = 1.1760825502

Simplifying
x = 1.1760825502


Subproblem 2
x + 0.2795918368 = -1.455674387

Simplifying
x + 0.2795918368 = -1.455674387

Reorder the terms:
0.2795918368 + x = -1.455674387

Solving
0.2795918368 + x = -1.455674387

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2795918368' to each side of the equation.
0.2795918368 + -0.2795918368 + x = -1.455674387 + -0.2795918368

Combine like terms: 0.2795918368 + -0.2795918368 = 0.0000000000
0.0000000000 + x = -1.455674387 + -0.2795918368
x = -1.455674387 + -0.2795918368

Combine like terms: -1.455674387 + -0.2795918368 = -1.7352662238
x = -1.7352662238

Simplifying
x = -1.7352662238


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1760825502, -1.7352662238}

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