10x^2-500x=-420

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Solution for 10x^2-500x=-420 equation:


Simplifying
10x2 + -500x = -420

Reorder the terms:
-500x + 10x2 = -420

Solving
-500x + 10x2 = -420

Solving for variable 'x'.

Reorder the terms:
420 + -500x + 10x2 = -420 + 420

Combine like terms: -420 + 420 = 0
420 + -500x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(42 + -50x + x2) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(42 + -50x + x2)' equal to zero and attempt to solve: Simplifying 42 + -50x + x2 = 0 Solving 42 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -50x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -50x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -50x + x2 = 0 + -42 -50x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -50x + x2 = -42 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -42 + 625 Reorder the terms: 625 + -50x + x2 = -42 + 625 Combine like terms: -42 + 625 = 583 625 + -50x + x2 = 583 Factor a perfect square on the left side: (x + -25)(x + -25) = 583 Calculate the square root of the right side: 24.145392935 Break this problem into two subproblems by setting (x + -25) equal to 24.145392935 and -24.145392935.

Subproblem 1

x + -25 = 24.145392935 Simplifying x + -25 = 24.145392935 Reorder the terms: -25 + x = 24.145392935 Solving -25 + x = 24.145392935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 24.145392935 + 25 Combine like terms: -25 + 25 = 0 0 + x = 24.145392935 + 25 x = 24.145392935 + 25 Combine like terms: 24.145392935 + 25 = 49.145392935 x = 49.145392935 Simplifying x = 49.145392935

Subproblem 2

x + -25 = -24.145392935 Simplifying x + -25 = -24.145392935 Reorder the terms: -25 + x = -24.145392935 Solving -25 + x = -24.145392935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -24.145392935 + 25 Combine like terms: -25 + 25 = 0 0 + x = -24.145392935 + 25 x = -24.145392935 + 25 Combine like terms: -24.145392935 + 25 = 0.854607065 x = 0.854607065 Simplifying x = 0.854607065

Solution

The solution to the problem is based on the solutions from the subproblems. x = {49.145392935, 0.854607065}

Solution

x = {49.145392935, 0.854607065}

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