-4.9x^2+10x+1.5=0

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Solution for -4.9x^2+10x+1.5=0 equation: 


Simplifying
-4.9x2 + 10x + 1.5 = 0

Reorder the terms:
1.5 + 10x + -4.9x2 = 0

Solving
1.5 + 10x + -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'.
-0.306122449 + -2.040816327x + x2 = 0

Move the constant term to the right:

Add '0.306122449' to each side of the equation.
-0.306122449 + -2.040816327x + 0.306122449 + x2 = 0 + 0.306122449

Reorder the terms:
-0.306122449 + 0.306122449 + -2.040816327x + x2 = 0 + 0.306122449

Combine like terms: -0.306122449 + 0.306122449 = 0.000000000
0.000000000 + -2.040816327x + x2 = 0 + 0.306122449
-2.040816327x + x2 = 0 + 0.306122449

Combine like terms: 0 + 0.306122449 = 0.306122449
-2.040816327x + x2 = 0.306122449

The x term is -2.040816327x.  Take half its coefficient (-1.020408164).
Square it (1.041232821) and add it to both sides.

Add '1.041232821' to each side of the equation.
-2.040816327x + 1.041232821 + x2 = 0.306122449 + 1.041232821

Reorder the terms:
1.041232821 + -2.040816327x + x2 = 0.306122449 + 1.041232821

Combine like terms: 0.306122449 + 1.041232821 = 1.34735527
1.041232821 + -2.040816327x + x2 = 1.34735527

Factor a perfect square on the left side:
(x + -1.020408164)(x + -1.020408164) = 1.34735527

Calculate the square root of the right side: 1.160756335

Break this problem into two subproblems by setting 
(x + -1.020408164) equal to 1.160756335 and -1.160756335.


Subproblem 1
x + -1.020408164 = 1.160756335

Simplifying
x + -1.020408164 = 1.160756335

Reorder the terms:
-1.020408164 + x = 1.160756335

Solving
-1.020408164 + x = 1.160756335

Solving for variable 'x'.

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

Add '1.020408164' to each side of the equation.
-1.020408164 + 1.020408164 + x = 1.160756335 + 1.020408164

Combine like terms: -1.020408164 + 1.020408164 = 0.000000000
0.000000000 + x = 1.160756335 + 1.020408164
x = 1.160756335 + 1.020408164

Combine like terms: 1.160756335 + 1.020408164 = 2.181164499
x = 2.181164499

Simplifying
x = 2.181164499


Subproblem 2
x + -1.020408164 = -1.160756335

Simplifying
x + -1.020408164 = -1.160756335

Reorder the terms:
-1.020408164 + x = -1.160756335

Solving
-1.020408164 + x = -1.160756335

Solving for variable 'x'.

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

Add '1.020408164' to each side of the equation.
-1.020408164 + 1.020408164 + x = -1.160756335 + 1.020408164

Combine like terms: -1.020408164 + 1.020408164 = 0.000000000
0.000000000 + x = -1.160756335 + 1.020408164
x = -1.160756335 + 1.020408164

Combine like terms: -1.160756335 + 1.020408164 = -0.140348171
x = -0.140348171

Simplifying
x = -0.140348171


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.181164499, -0.140348171}

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