100x-2x^2=100

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Solution for 100x-2x^2=100 equation:


Simplifying
100x + -2x2 = 100

Solving
100x + -2x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 100x + -2x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 100x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 50x + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-50 + 50x + -1x2)' equal to zero and attempt to solve: Simplifying -50 + 50x + -1x2 = 0 Solving -50 + 50x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 50 + -50x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -50x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -50x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -50x + x2 = 0 + -50 -50x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -50x + x2 = -50 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 = -50 + 625 Reorder the terms: 625 + -50x + x2 = -50 + 625 Combine like terms: -50 + 625 = 575 625 + -50x + x2 = 575 Factor a perfect square on the left side: (x + -25)(x + -25) = 575 Calculate the square root of the right side: 23.979157617 Break this problem into two subproblems by setting (x + -25) equal to 23.979157617 and -23.979157617.

Subproblem 1

x + -25 = 23.979157617 Simplifying x + -25 = 23.979157617 Reorder the terms: -25 + x = 23.979157617 Solving -25 + x = 23.979157617 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 = 23.979157617 + 25 Combine like terms: -25 + 25 = 0 0 + x = 23.979157617 + 25 x = 23.979157617 + 25 Combine like terms: 23.979157617 + 25 = 48.979157617 x = 48.979157617 Simplifying x = 48.979157617

Subproblem 2

x + -25 = -23.979157617 Simplifying x + -25 = -23.979157617 Reorder the terms: -25 + x = -23.979157617 Solving -25 + x = -23.979157617 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 = -23.979157617 + 25 Combine like terms: -25 + 25 = 0 0 + x = -23.979157617 + 25 x = -23.979157617 + 25 Combine like terms: -23.979157617 + 25 = 1.020842383 x = 1.020842383 Simplifying x = 1.020842383

Solution

The solution to the problem is based on the solutions from the subproblems. x = {48.979157617, 1.020842383}

Solution

x = {48.979157617, 1.020842383}

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