(x-40)(x+100)=.375

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Solution for (x-40)(x+100)=.375 equation:


Simplifying
(x + -40)(x + 100) = 0.375

Reorder the terms:
(-40 + x)(x + 100) = 0.375

Reorder the terms:
(-40 + x)(100 + x) = 0.375

Multiply (-40 + x) * (100 + x)
(-40(100 + x) + x(100 + x)) = 0.375
((100 * -40 + x * -40) + x(100 + x)) = 0.375
((-4000 + -40x) + x(100 + x)) = 0.375
(-4000 + -40x + (100 * x + x * x)) = 0.375
(-4000 + -40x + (100x + x2)) = 0.375

Combine like terms: -40x + 100x = 60x
(-4000 + 60x + x2) = 0.375

Solving
-4000 + 60x + x2 = 0.375

Solving for variable 'x'.

Reorder the terms:
-4000 + -0.375 + 60x + x2 = 0.375 + -0.375

Combine like terms: -4000 + -0.375 = -4000.375
-4000.375 + 60x + x2 = 0.375 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
-4000.375 + 60x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '4000.375' to each side of the equation.
-4000.375 + 60x + 4000.375 + x2 = 0.000 + 4000.375

Reorder the terms:
-4000.375 + 4000.375 + 60x + x2 = 0.000 + 4000.375

Combine like terms: -4000.375 + 4000.375 = 0.000
0.000 + 60x + x2 = 0.000 + 4000.375
60x + x2 = 0.000 + 4000.375

Combine like terms: 0.000 + 4000.375 = 4000.375
60x + x2 = 4000.375

The x term is 60x.  Take half its coefficient (30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
60x + 900 + x2 = 4000.375 + 900

Reorder the terms:
900 + 60x + x2 = 4000.375 + 900

Combine like terms: 4000.375 + 900 = 4900.375
900 + 60x + x2 = 4900.375

Factor a perfect square on the left side:
(x + 30)(x + 30) = 4900.375

Calculate the square root of the right side: 70.00267852

Break this problem into two subproblems by setting 
(x + 30) equal to 70.00267852 and -70.00267852.

Subproblem 1

x + 30 = 70.00267852 Simplifying x + 30 = 70.00267852 Reorder the terms: 30 + x = 70.00267852 Solving 30 + x = 70.00267852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 70.00267852 + -30 Combine like terms: 30 + -30 = 0 0 + x = 70.00267852 + -30 x = 70.00267852 + -30 Combine like terms: 70.00267852 + -30 = 40.00267852 x = 40.00267852 Simplifying x = 40.00267852

Subproblem 2

x + 30 = -70.00267852 Simplifying x + 30 = -70.00267852 Reorder the terms: 30 + x = -70.00267852 Solving 30 + x = -70.00267852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -70.00267852 + -30 Combine like terms: 30 + -30 = 0 0 + x = -70.00267852 + -30 x = -70.00267852 + -30 Combine like terms: -70.00267852 + -30 = -100.00267852 x = -100.00267852 Simplifying x = -100.00267852

Solution

The solution to the problem is based on the solutions from the subproblems. x = {40.00267852, -100.00267852}

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