2.5x^2+1.5x-5=0

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Solution for 2.5x^2+1.5x-5=0 equation:


Simplifying
2.5x2 + 1.5x + -5 = 0

Reorder the terms:
-5 + 1.5x + 2.5x2 = 0

Solving
-5 + 1.5x + 2.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.5'.
-2 + 0.6x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.6x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.6x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.6x + x2 = 0 + 2
0.6x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.6x + x2 = 2

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 = 2 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 2 + 0.09

Combine like terms: 2 + 0.09 = 2.09
0.09 + 0.6x + x2 = 2.09

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 2.09

Calculate the square root of the right side: 1.445683229

Break this problem into two subproblems by setting 
(x + 0.3) equal to 1.445683229 and -1.445683229.

Subproblem 1

x + 0.3 = 1.445683229 Simplifying x + 0.3 = 1.445683229 Reorder the terms: 0.3 + x = 1.445683229 Solving 0.3 + x = 1.445683229 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 = 1.445683229 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.445683229 + -0.3 x = 1.445683229 + -0.3 Combine like terms: 1.445683229 + -0.3 = 1.145683229 x = 1.145683229 Simplifying x = 1.145683229

Subproblem 2

x + 0.3 = -1.445683229 Simplifying x + 0.3 = -1.445683229 Reorder the terms: 0.3 + x = -1.445683229 Solving 0.3 + x = -1.445683229 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 = -1.445683229 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.445683229 + -0.3 x = -1.445683229 + -0.3 Combine like terms: -1.445683229 + -0.3 = -1.745683229 x = -1.745683229 Simplifying x = -1.745683229

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.145683229, -1.745683229}

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