-2x(x-3)+5x=-15

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Solution for -2x(x-3)+5x=-15 equation:


Simplifying
-2x(x + -3) + 5x = -15

Reorder the terms:
-2x(-3 + x) + 5x = -15
(-3 * -2x + x * -2x) + 5x = -15
(6x + -2x2) + 5x = -15

Reorder the terms:
6x + 5x + -2x2 = -15

Combine like terms: 6x + 5x = 11x
11x + -2x2 = -15

Solving
11x + -2x2 = -15

Solving for variable 'x'.

Reorder the terms:
15 + 11x + -2x2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + 11x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-7.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -5.5x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -5.5x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -5.5x + x2 = 0 + 7.5
-5.5x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-5.5x + x2 = 7.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 7.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 7.5 + 7.5625

Combine like terms: 7.5 + 7.5625 = 15.0625
7.5625 + -5.5x + x2 = 15.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 15.0625

Calculate the square root of the right side: 3.881043674

Break this problem into two subproblems by setting 
(x + -2.75) equal to 3.881043674 and -3.881043674.

Subproblem 1

x + -2.75 = 3.881043674 Simplifying x + -2.75 = 3.881043674 Reorder the terms: -2.75 + x = 3.881043674 Solving -2.75 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.881043674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.881043674 + 2.75 x = 3.881043674 + 2.75 Combine like terms: 3.881043674 + 2.75 = 6.631043674 x = 6.631043674 Simplifying x = 6.631043674

Subproblem 2

x + -2.75 = -3.881043674 Simplifying x + -2.75 = -3.881043674 Reorder the terms: -2.75 + x = -3.881043674 Solving -2.75 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.881043674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.881043674 + 2.75 x = -3.881043674 + 2.75 Combine like terms: -3.881043674 + 2.75 = -1.131043674 x = -1.131043674 Simplifying x = -1.131043674

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.631043674, -1.131043674}

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