2.5x(x+2)+4.5+1.5(x-3)=15

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Solution for 2.5x(x+2)+4.5+1.5(x-3)=15 equation:


Simplifying
2.5x(x + 2) + 4.5 + 1.5(x + -3) = 15

Reorder the terms:
2.5x(2 + x) + 4.5 + 1.5(x + -3) = 15
(2 * 2.5x + x * 2.5x) + 4.5 + 1.5(x + -3) = 15
(5x + 2.5x2) + 4.5 + 1.5(x + -3) = 15

Reorder the terms:
5x + 2.5x2 + 4.5 + 1.5(-3 + x) = 15
5x + 2.5x2 + 4.5 + (-3 * 1.5 + x * 1.5) = 15
5x + 2.5x2 + 4.5 + (-4.5 + 1.5x) = 15

Reorder the terms:
4.5 + -4.5 + 5x + 1.5x + 2.5x2 = 15

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 5x + 1.5x + 2.5x2 = 15
5x + 1.5x + 2.5x2 = 15

Combine like terms: 5x + 1.5x = 6.5x
6.5x + 2.5x2 = 15

Solving
6.5x + 2.5x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + 6.5x + 2.5x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 6.5x + 2.5x2 = 0

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

Divide each side by '2.5'.
-6 + 2.6x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2.6x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 2.6x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2.6x + x2 = 0 + 6
2.6x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
2.6x + x2 = 6

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = 6 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = 6 + 1.69

Combine like terms: 6 + 1.69 = 7.69
1.69 + 2.6x + x2 = 7.69

Factor a perfect square on the left side:
(x + 1.3)(x + 1.3) = 7.69

Calculate the square root of the right side: 2.773084925

Break this problem into two subproblems by setting 
(x + 1.3) equal to 2.773084925 and -2.773084925.

Subproblem 1

x + 1.3 = 2.773084925 Simplifying x + 1.3 = 2.773084925 Reorder the terms: 1.3 + x = 2.773084925 Solving 1.3 + x = 2.773084925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 2.773084925 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 2.773084925 + -1.3 x = 2.773084925 + -1.3 Combine like terms: 2.773084925 + -1.3 = 1.473084925 x = 1.473084925 Simplifying x = 1.473084925

Subproblem 2

x + 1.3 = -2.773084925 Simplifying x + 1.3 = -2.773084925 Reorder the terms: 1.3 + x = -2.773084925 Solving 1.3 + x = -2.773084925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -2.773084925 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -2.773084925 + -1.3 x = -2.773084925 + -1.3 Combine like terms: -2.773084925 + -1.3 = -4.073084925 x = -4.073084925 Simplifying x = -4.073084925

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.473084925, -4.073084925}

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