50+10x-4.9x^2=0

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Solution for 50+10x-4.9x^2=0 equation:


Simplifying
50 + 10x + -4.9x2 = 0

Solving
50 + 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'.
-10.20408163 + -2.040816327x + x2 = 0

Move the constant term to the right:

Add '10.20408163' to each side of the equation.
-10.20408163 + -2.040816327x + 10.20408163 + x2 = 0 + 10.20408163

Reorder the terms:
-10.20408163 + 10.20408163 + -2.040816327x + x2 = 0 + 10.20408163

Combine like terms: -10.20408163 + 10.20408163 = 0.00000000
0.00000000 + -2.040816327x + x2 = 0 + 10.20408163
-2.040816327x + x2 = 0 + 10.20408163

Combine like terms: 0 + 10.20408163 = 10.20408163
-2.040816327x + x2 = 10.20408163

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 = 10.20408163 + 1.041232821

Reorder the terms:
1.041232821 + -2.040816327x + x2 = 10.20408163 + 1.041232821

Combine like terms: 10.20408163 + 1.041232821 = 11.245314451
1.041232821 + -2.040816327x + x2 = 11.245314451

Factor a perfect square on the left side:
(x + -1.020408164)(x + -1.020408164) = 11.245314451

Calculate the square root of the right side: 3.353403413

Break this problem into two subproblems by setting 
(x + -1.020408164) equal to 3.353403413 and -3.353403413.

Subproblem 1

x + -1.020408164 = 3.353403413 Simplifying x + -1.020408164 = 3.353403413 Reorder the terms: -1.020408164 + x = 3.353403413 Solving -1.020408164 + x = 3.353403413 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 = 3.353403413 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 3.353403413 + 1.020408164 x = 3.353403413 + 1.020408164 Combine like terms: 3.353403413 + 1.020408164 = 4.373811577 x = 4.373811577 Simplifying x = 4.373811577

Subproblem 2

x + -1.020408164 = -3.353403413 Simplifying x + -1.020408164 = -3.353403413 Reorder the terms: -1.020408164 + x = -3.353403413 Solving -1.020408164 + x = -3.353403413 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 = -3.353403413 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -3.353403413 + 1.020408164 x = -3.353403413 + 1.020408164 Combine like terms: -3.353403413 + 1.020408164 = -2.332995249 x = -2.332995249 Simplifying x = -2.332995249

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.373811577, -2.332995249}

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