-40x+x^2=450

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Solution for -40x+x^2=450 equation:


Simplifying
-40x + x2 = 450

Solving
-40x + x2 = 450

Solving for variable 'x'.

Reorder the terms:
-450 + -40x + x2 = 450 + -450

Combine like terms: 450 + -450 = 0
-450 + -40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '450' to each side of the equation.
-450 + -40x + 450 + x2 = 0 + 450

Reorder the terms:
-450 + 450 + -40x + x2 = 0 + 450

Combine like terms: -450 + 450 = 0
0 + -40x + x2 = 0 + 450
-40x + x2 = 0 + 450

Combine like terms: 0 + 450 = 450
-40x + x2 = 450

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 450 + 400

Reorder the terms:
400 + -40x + x2 = 450 + 400

Combine like terms: 450 + 400 = 850
400 + -40x + x2 = 850

Factor a perfect square on the left side:
(x + -20)(x + -20) = 850

Calculate the square root of the right side: 29.154759474

Break this problem into two subproblems by setting 
(x + -20) equal to 29.154759474 and -29.154759474.

Subproblem 1

x + -20 = 29.154759474 Simplifying x + -20 = 29.154759474 Reorder the terms: -20 + x = 29.154759474 Solving -20 + x = 29.154759474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 29.154759474 + 20 Combine like terms: -20 + 20 = 0 0 + x = 29.154759474 + 20 x = 29.154759474 + 20 Combine like terms: 29.154759474 + 20 = 49.154759474 x = 49.154759474 Simplifying x = 49.154759474

Subproblem 2

x + -20 = -29.154759474 Simplifying x + -20 = -29.154759474 Reorder the terms: -20 + x = -29.154759474 Solving -20 + x = -29.154759474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -29.154759474 + 20 Combine like terms: -20 + 20 = 0 0 + x = -29.154759474 + 20 x = -29.154759474 + 20 Combine like terms: -29.154759474 + 20 = -9.154759474 x = -9.154759474 Simplifying x = -9.154759474

Solution

The solution to the problem is based on the solutions from the subproblems. x = {49.154759474, -9.154759474}

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