100x^2-1700x+800=0

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Solution for 100x^2-1700x+800=0 equation:


Simplifying
100x2 + -1700x + 800 = 0

Reorder the terms:
800 + -1700x + 100x2 = 0

Solving
800 + -1700x + 100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '100'.
100(8 + -17x + x2) = 0

Ignore the factor 100.

Subproblem 1

Set the factor '(8 + -17x + x2)' equal to zero and attempt to solve: Simplifying 8 + -17x + x2 = 0 Solving 8 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -17x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -17x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -17x + x2 = 0 + -8 -17x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -17x + x2 = -8 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -8 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -8 + 72.25 Combine like terms: -8 + 72.25 = 64.25 72.25 + -17x + x2 = 64.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + -8.5) equal to 8.015609771 and -8.015609771.

Subproblem 1

x + -8.5 = 8.015609771 Simplifying x + -8.5 = 8.015609771 Reorder the terms: -8.5 + x = 8.015609771 Solving -8.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 8.015609771 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.015609771 + 8.5 x = 8.015609771 + 8.5 Combine like terms: 8.015609771 + 8.5 = 16.515609771 x = 16.515609771 Simplifying x = 16.515609771

Subproblem 2

x + -8.5 = -8.015609771 Simplifying x + -8.5 = -8.015609771 Reorder the terms: -8.5 + x = -8.015609771 Solving -8.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -8.015609771 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.015609771 + 8.5 x = -8.015609771 + 8.5 Combine like terms: -8.015609771 + 8.5 = 0.484390229 x = 0.484390229 Simplifying x = 0.484390229

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.515609771, 0.484390229}

Solution

x = {16.515609771, 0.484390229}

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