-5x^2+15x+2=0

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Solution for -5x^2+15x+2=0 equation:


Simplifying
-5x2 + 15x + 2 = 0

Reorder the terms:
2 + 15x + -5x2 = 0

Solving
2 + 15x + -5x2 = 0

Solving for variable 'x'.

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

Divide each side by '-5'.
-0.4 + -3x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -3x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -3x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -3x + x2 = 0 + 0.4
-3x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-3x + x2 = 0.4

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 = 0.4 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 0.4 + 2.25

Combine like terms: 0.4 + 2.25 = 2.65
2.25 + -3x + x2 = 2.65

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 2.65

Calculate the square root of the right side: 1.62788206

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.62788206 and -1.62788206.

Subproblem 1

x + -1.5 = 1.62788206 Simplifying x + -1.5 = 1.62788206 Reorder the terms: -1.5 + x = 1.62788206 Solving -1.5 + x = 1.62788206 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 = 1.62788206 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.62788206 + 1.5 x = 1.62788206 + 1.5 Combine like terms: 1.62788206 + 1.5 = 3.12788206 x = 3.12788206 Simplifying x = 3.12788206

Subproblem 2

x + -1.5 = -1.62788206 Simplifying x + -1.5 = -1.62788206 Reorder the terms: -1.5 + x = -1.62788206 Solving -1.5 + x = -1.62788206 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 = -1.62788206 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.62788206 + 1.5 x = -1.62788206 + 1.5 Combine like terms: -1.62788206 + 1.5 = -0.12788206 x = -0.12788206 Simplifying x = -0.12788206

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.12788206, -0.12788206}

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