4x^2+4.5x-2.25=0

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Solution for 4x^2+4.5x-2.25=0 equation:


Simplifying
4x2 + 4.5x + -2.25 = 0

Reorder the terms:
-2.25 + 4.5x + 4x2 = 0

Solving
-2.25 + 4.5x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-0.5625 + 1.125x + x2 = 0

Move the constant term to the right:

Add '0.5625' to each side of the equation.
-0.5625 + 1.125x + 0.5625 + x2 = 0 + 0.5625

Reorder the terms:
-0.5625 + 0.5625 + 1.125x + x2 = 0 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + 1.125x + x2 = 0 + 0.5625
1.125x + x2 = 0 + 0.5625

Combine like terms: 0 + 0.5625 = 0.5625
1.125x + x2 = 0.5625

The x term is 1.125x.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125x + 0.31640625 + x2 = 0.5625 + 0.31640625

Reorder the terms:
0.31640625 + 1.125x + x2 = 0.5625 + 0.31640625

Combine like terms: 0.5625 + 0.31640625 = 0.87890625
0.31640625 + 1.125x + x2 = 0.87890625

Factor a perfect square on the left side:
(x + 0.5625)(x + 0.5625) = 0.87890625

Calculate the square root of the right side: 0.9375

Break this problem into two subproblems by setting 
(x + 0.5625) equal to 0.9375 and -0.9375.

Subproblem 1

x + 0.5625 = 0.9375 Simplifying x + 0.5625 = 0.9375 Reorder the terms: 0.5625 + x = 0.9375 Solving 0.5625 + x = 0.9375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 0.9375 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 0.9375 + -0.5625 x = 0.9375 + -0.5625 Combine like terms: 0.9375 + -0.5625 = 0.375 x = 0.375 Simplifying x = 0.375

Subproblem 2

x + 0.5625 = -0.9375 Simplifying x + 0.5625 = -0.9375 Reorder the terms: 0.5625 + x = -0.9375 Solving 0.5625 + x = -0.9375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -0.9375 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -0.9375 + -0.5625 x = -0.9375 + -0.5625 Combine like terms: -0.9375 + -0.5625 = -1.5 x = -1.5 Simplifying x = -1.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.375, -1.5}

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