5x^2+15x+56.25=64.25

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Solution for 5x^2+15x+56.25=64.25 equation:


Simplifying
5x2 + 15x + 56.25 = 64.25

Reorder the terms:
56.25 + 15x + 5x2 = 64.25

Solving
56.25 + 15x + 5x2 = 64.25

Solving for variable 'x'.

Reorder the terms:
56.25 + -64.25 + 15x + 5x2 = 64.25 + -64.25

Combine like terms: 56.25 + -64.25 = -8
-8 + 15x + 5x2 = 64.25 + -64.25

Combine like terms: 64.25 + -64.25 = 0.00
-8 + 15x + 5x2 = 0.00

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

Divide each side by '5'.
-1.6 + 3x + x2 = 0.00

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 3x + 1.6 + x2 = 0.00 + 1.6

Reorder the terms:
-1.6 + 1.6 + 3x + x2 = 0.00 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 3x + x2 = 0.00 + 1.6
3x + x2 = 0.00 + 1.6

Combine like terms: 0.00 + 1.6 = 1.6
3x + x2 = 1.6

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 1.6 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1.6 + 2.25

Combine like terms: 1.6 + 2.25 = 3.85
2.25 + 3x + x2 = 3.85

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 3.85

Calculate the square root of the right side: 1.962141687

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.962141687 and -1.962141687.

Subproblem 1

x + 1.5 = 1.962141687 Simplifying x + 1.5 = 1.962141687 Reorder the terms: 1.5 + x = 1.962141687 Solving 1.5 + x = 1.962141687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.962141687 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.962141687 + -1.5 x = 1.962141687 + -1.5 Combine like terms: 1.962141687 + -1.5 = 0.462141687 x = 0.462141687 Simplifying x = 0.462141687

Subproblem 2

x + 1.5 = -1.962141687 Simplifying x + 1.5 = -1.962141687 Reorder the terms: 1.5 + x = -1.962141687 Solving 1.5 + x = -1.962141687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.962141687 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.962141687 + -1.5 x = -1.962141687 + -1.5 Combine like terms: -1.962141687 + -1.5 = -3.462141687 x = -3.462141687 Simplifying x = -3.462141687

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.462141687, -3.462141687}

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