x^2+2.25x-.6=0

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Solution for x^2+2.25x-.6=0 equation:


Simplifying
x2 + 2.25x + -0.6 = 0

Reorder the terms:
-0.6 + 2.25x + x2 = 0

Solving
-0.6 + 2.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 2.25x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 2.25x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 2.25x + x2 = 0 + 0.6
2.25x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
2.25x + x2 = 0.6

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = 0.6 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 0.6 + 1.265625

Combine like terms: 0.6 + 1.265625 = 1.865625
1.265625 + 2.25x + x2 = 1.865625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 1.865625

Calculate the square root of the right side: 1.365878838

Break this problem into two subproblems by setting 
(x + 1.125) equal to 1.365878838 and -1.365878838.

Subproblem 1

x + 1.125 = 1.365878838 Simplifying x + 1.125 = 1.365878838 Reorder the terms: 1.125 + x = 1.365878838 Solving 1.125 + x = 1.365878838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 1.365878838 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.365878838 + -1.125 x = 1.365878838 + -1.125 Combine like terms: 1.365878838 + -1.125 = 0.240878838 x = 0.240878838 Simplifying x = 0.240878838

Subproblem 2

x + 1.125 = -1.365878838 Simplifying x + 1.125 = -1.365878838 Reorder the terms: 1.125 + x = -1.365878838 Solving 1.125 + x = -1.365878838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -1.365878838 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.365878838 + -1.125 x = -1.365878838 + -1.125 Combine like terms: -1.365878838 + -1.125 = -2.490878838 x = -2.490878838 Simplifying x = -2.490878838

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.240878838, -2.490878838}

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