-4.9x^2+21.28x-15=0

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Solution for -4.9x^2+21.28x-15=0 equation:


Simplifying
-4.9x2 + 21.28x + -15 = 0

Reorder the terms:
-15 + 21.28x + -4.9x2 = 0

Solving
-15 + 21.28x + -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'.
3.06122449 + -4.342857143x + x2 = 0

Move the constant term to the right:

Add '-3.06122449' to each side of the equation.
3.06122449 + -4.342857143x + -3.06122449 + x2 = 0 + -3.06122449

Reorder the terms:
3.06122449 + -3.06122449 + -4.342857143x + x2 = 0 + -3.06122449

Combine like terms: 3.06122449 + -3.06122449 = 0.00000000
0.00000000 + -4.342857143x + x2 = 0 + -3.06122449
-4.342857143x + x2 = 0 + -3.06122449

Combine like terms: 0 + -3.06122449 = -3.06122449
-4.342857143x + x2 = -3.06122449

The x term is -4.342857143x.  Take half its coefficient (-2.171428572).
Square it (4.715102043) and add it to both sides.

Add '4.715102043' to each side of the equation.
-4.342857143x + 4.715102043 + x2 = -3.06122449 + 4.715102043

Reorder the terms:
4.715102043 + -4.342857143x + x2 = -3.06122449 + 4.715102043

Combine like terms: -3.06122449 + 4.715102043 = 1.653877553
4.715102043 + -4.342857143x + x2 = 1.653877553

Factor a perfect square on the left side:
(x + -2.171428572)(x + -2.171428572) = 1.653877553

Calculate the square root of the right side: 1.286031708

Break this problem into two subproblems by setting 
(x + -2.171428572) equal to 1.286031708 and -1.286031708.

Subproblem 1

x + -2.171428572 = 1.286031708 Simplifying x + -2.171428572 = 1.286031708 Reorder the terms: -2.171428572 + x = 1.286031708 Solving -2.171428572 + x = 1.286031708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.171428572' to each side of the equation. -2.171428572 + 2.171428572 + x = 1.286031708 + 2.171428572 Combine like terms: -2.171428572 + 2.171428572 = 0.000000000 0.000000000 + x = 1.286031708 + 2.171428572 x = 1.286031708 + 2.171428572 Combine like terms: 1.286031708 + 2.171428572 = 3.45746028 x = 3.45746028 Simplifying x = 3.45746028

Subproblem 2

x + -2.171428572 = -1.286031708 Simplifying x + -2.171428572 = -1.286031708 Reorder the terms: -2.171428572 + x = -1.286031708 Solving -2.171428572 + x = -1.286031708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.171428572' to each side of the equation. -2.171428572 + 2.171428572 + x = -1.286031708 + 2.171428572 Combine like terms: -2.171428572 + 2.171428572 = 0.000000000 0.000000000 + x = -1.286031708 + 2.171428572 x = -1.286031708 + 2.171428572 Combine like terms: -1.286031708 + 2.171428572 = 0.885396864 x = 0.885396864 Simplifying x = 0.885396864

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.45746028, 0.885396864}

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