4.9*x^2-6.5*x=15

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Solution for 4.9*x^2-6.5*x=15 equation:


Simplifying
4.9x2 + -6.5x = 15

Reorder the terms:
-6.5x + 4.9x2 = 15

Solving
-6.5x + 4.9x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -6.5x + 4.9x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -6.5x + 4.9x2 = 0

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

Divide each side by '4.9'.
-3.06122449 + -1.326530612x + x2 = 0

Move the constant term to the right:

Add '3.06122449' to each side of the equation.
-3.06122449 + -1.326530612x + 3.06122449 + x2 = 0 + 3.06122449

Reorder the terms:
-3.06122449 + 3.06122449 + -1.326530612x + x2 = 0 + 3.06122449

Combine like terms: -3.06122449 + 3.06122449 = 0.00000000
0.00000000 + -1.326530612x + x2 = 0 + 3.06122449
-1.326530612x + x2 = 0 + 3.06122449

Combine like terms: 0 + 3.06122449 = 3.06122449
-1.326530612x + x2 = 3.06122449

The x term is -1.326530612x.  Take half its coefficient (-0.663265306).
Square it (0.4399208661) and add it to both sides.

Add '0.4399208661' to each side of the equation.
-1.326530612x + 0.4399208661 + x2 = 3.06122449 + 0.4399208661

Reorder the terms:
0.4399208661 + -1.326530612x + x2 = 3.06122449 + 0.4399208661

Combine like terms: 3.06122449 + 0.4399208661 = 3.5011453561
0.4399208661 + -1.326530612x + x2 = 3.5011453561

Factor a perfect square on the left side:
(x + -0.663265306)(x + -0.663265306) = 3.5011453561

Calculate the square root of the right side: 1.871134778

Break this problem into two subproblems by setting 
(x + -0.663265306) equal to 1.871134778 and -1.871134778.

Subproblem 1

x + -0.663265306 = 1.871134778 Simplifying x + -0.663265306 = 1.871134778 Reorder the terms: -0.663265306 + x = 1.871134778 Solving -0.663265306 + x = 1.871134778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.663265306' to each side of the equation. -0.663265306 + 0.663265306 + x = 1.871134778 + 0.663265306 Combine like terms: -0.663265306 + 0.663265306 = 0.000000000 0.000000000 + x = 1.871134778 + 0.663265306 x = 1.871134778 + 0.663265306 Combine like terms: 1.871134778 + 0.663265306 = 2.534400084 x = 2.534400084 Simplifying x = 2.534400084

Subproblem 2

x + -0.663265306 = -1.871134778 Simplifying x + -0.663265306 = -1.871134778 Reorder the terms: -0.663265306 + x = -1.871134778 Solving -0.663265306 + x = -1.871134778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.663265306' to each side of the equation. -0.663265306 + 0.663265306 + x = -1.871134778 + 0.663265306 Combine like terms: -0.663265306 + 0.663265306 = 0.000000000 0.000000000 + x = -1.871134778 + 0.663265306 x = -1.871134778 + 0.663265306 Combine like terms: -1.871134778 + 0.663265306 = -1.207869472 x = -1.207869472 Simplifying x = -1.207869472

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.534400084, -1.207869472}

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