(x+0.3)(x-0.4)=

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Solution for (x+0.3)(x-0.4)= equation:


Simplifying
(x + 0.3)(x + -0.4) = 0

Reorder the terms:
(0.3 + x)(x + -0.4) = 0

Reorder the terms:
(0.3 + x)(-0.4 + x) = 0

Multiply (0.3 + x) * (-0.4 + x)
(0.3(-0.4 + x) + x(-0.4 + x)) = 0
((-0.4 * 0.3 + x * 0.3) + x(-0.4 + x)) = 0
((-0.12 + 0.3x) + x(-0.4 + x)) = 0
(-0.12 + 0.3x + (-0.4 * x + x * x)) = 0
(-0.12 + 0.3x + (-0.4x + x2)) = 0

Combine like terms: 0.3x + -0.4x = -0.1x
(-0.12 + -0.1x + x2) = 0

Solving
-0.12 + -0.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.12' to each side of the equation.
-0.12 + -0.1x + 0.12 + x2 = 0 + 0.12

Reorder the terms:
-0.12 + 0.12 + -0.1x + x2 = 0 + 0.12

Combine like terms: -0.12 + 0.12 = 0.00
0.00 + -0.1x + x2 = 0 + 0.12
-0.1x + x2 = 0 + 0.12

Combine like terms: 0 + 0.12 = 0.12
-0.1x + x2 = 0.12

The x term is -0.1x.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1x + 0.0025 + x2 = 0.12 + 0.0025

Reorder the terms:
0.0025 + -0.1x + x2 = 0.12 + 0.0025

Combine like terms: 0.12 + 0.0025 = 0.1225
0.0025 + -0.1x + x2 = 0.1225

Factor a perfect square on the left side:
(x + -0.05)(x + -0.05) = 0.1225

Calculate the square root of the right side: 0.35

Break this problem into two subproblems by setting 
(x + -0.05) equal to 0.35 and -0.35.

Subproblem 1

x + -0.05 = 0.35 Simplifying x + -0.05 = 0.35 Reorder the terms: -0.05 + x = 0.35 Solving -0.05 + x = 0.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 0.35 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 0.35 + 0.05 x = 0.35 + 0.05 Combine like terms: 0.35 + 0.05 = 0.4 x = 0.4 Simplifying x = 0.4

Subproblem 2

x + -0.05 = -0.35 Simplifying x + -0.05 = -0.35 Reorder the terms: -0.05 + x = -0.35 Solving -0.05 + x = -0.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -0.35 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -0.35 + 0.05 x = -0.35 + 0.05 Combine like terms: -0.35 + 0.05 = -0.3 x = -0.3 Simplifying x = -0.3

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4, -0.3}

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