x*x+0.3x-0.54=

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Solution for x*x+0.3x-0.54= equation:


Simplifying
x * x + 0.3x + -0.54 = 0

Multiply x * x
x2 + 0.3x + -0.54 = 0

Reorder the terms:
-0.54 + 0.3x + x2 = 0

Solving
-0.54 + 0.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.54' to each side of the equation.
-0.54 + 0.3x + 0.54 + x2 = 0 + 0.54

Reorder the terms:
-0.54 + 0.54 + 0.3x + x2 = 0 + 0.54

Combine like terms: -0.54 + 0.54 = 0.00
0.00 + 0.3x + x2 = 0 + 0.54
0.3x + x2 = 0 + 0.54

Combine like terms: 0 + 0.54 = 0.54
0.3x + x2 = 0.54

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 0.54 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 0.54 + 0.0225

Combine like terms: 0.54 + 0.0225 = 0.5625
0.0225 + 0.3x + x2 = 0.5625

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 0.5625

Calculate the square root of the right side: 0.75

Break this problem into two subproblems by setting 
(x + 0.15) equal to 0.75 and -0.75.

Subproblem 1

x + 0.15 = 0.75 Simplifying x + 0.15 = 0.75 Reorder the terms: 0.15 + x = 0.75 Solving 0.15 + x = 0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.75 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.75 + -0.15 x = 0.75 + -0.15 Combine like terms: 0.75 + -0.15 = 0.6 x = 0.6 Simplifying x = 0.6

Subproblem 2

x + 0.15 = -0.75 Simplifying x + 0.15 = -0.75 Reorder the terms: 0.15 + x = -0.75 Solving 0.15 + x = -0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.75 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.75 + -0.15 x = -0.75 + -0.15 Combine like terms: -0.75 + -0.15 = -0.9 x = -0.9 Simplifying x = -0.9

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6, -0.9}

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