5x^2+3x-15=0

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Solution for 5x^2+3x-15=0 equation:


Simplifying
5x2 + 3x + -15 = 0

Reorder the terms:
-15 + 3x + 5x2 = 0

Solving
-15 + 3x + 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'.
-3 + 0.6x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 0.6x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 0.6x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 0.6x + x2 = 0 + 3
0.6x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
0.6x + x2 = 3

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 3 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 3 + 0.09

Combine like terms: 3 + 0.09 = 3.09
0.09 + 0.6x + x2 = 3.09

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 3.09

Calculate the square root of the right side: 1.757839583

Break this problem into two subproblems by setting 
(x + 0.3) equal to 1.757839583 and -1.757839583.

Subproblem 1

x + 0.3 = 1.757839583 Simplifying x + 0.3 = 1.757839583 Reorder the terms: 0.3 + x = 1.757839583 Solving 0.3 + x = 1.757839583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1.757839583 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.757839583 + -0.3 x = 1.757839583 + -0.3 Combine like terms: 1.757839583 + -0.3 = 1.457839583 x = 1.457839583 Simplifying x = 1.457839583

Subproblem 2

x + 0.3 = -1.757839583 Simplifying x + 0.3 = -1.757839583 Reorder the terms: 0.3 + x = -1.757839583 Solving 0.3 + x = -1.757839583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1.757839583 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.757839583 + -0.3 x = -1.757839583 + -0.3 Combine like terms: -1.757839583 + -0.3 = -2.057839583 x = -2.057839583 Simplifying x = -2.057839583

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.457839583, -2.057839583}

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