900=10x^2-20x

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Solution for 900=10x^2-20x equation:


Simplifying
900 = 10x2 + -20x

Reorder the terms:
900 = -20x + 10x2

Solving
900 = -20x + 10x2

Solving for variable 'x'.

Reorder the terms:
900 + 20x + -10x2 = -20x + 20x + 10x2 + -10x2

Combine like terms: -20x + 20x = 0
900 + 20x + -10x2 = 0 + 10x2 + -10x2
900 + 20x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
900 + 20x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(90 + 2x + -1x2) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(90 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 90 + 2x + -1x2 = 0 Solving 90 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -90 + -2x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + -2x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -2x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -2x + x2 = 0 + 90 -2x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -2x + x2 = 90 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 90 + 1 Reorder the terms: 1 + -2x + x2 = 90 + 1 Combine like terms: 90 + 1 = 91 1 + -2x + x2 = 91 Factor a perfect square on the left side: (x + -1)(x + -1) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + -1) equal to 9.539392014 and -9.539392014.

Subproblem 1

x + -1 = 9.539392014 Simplifying x + -1 = 9.539392014 Reorder the terms: -1 + x = 9.539392014 Solving -1 + x = 9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 9.539392014 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.539392014 + 1 x = 9.539392014 + 1 Combine like terms: 9.539392014 + 1 = 10.539392014 x = 10.539392014 Simplifying x = 10.539392014

Subproblem 2

x + -1 = -9.539392014 Simplifying x + -1 = -9.539392014 Reorder the terms: -1 + x = -9.539392014 Solving -1 + x = -9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -9.539392014 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.539392014 + 1 x = -9.539392014 + 1 Combine like terms: -9.539392014 + 1 = -8.539392014 x = -8.539392014 Simplifying x = -8.539392014

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.539392014, -8.539392014}

Solution

x = {10.539392014, -8.539392014}

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