9565=x^2-5x+65

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Solution for 9565=x^2-5x+65 equation:


Simplifying
9565 = x2 + -5x + 65

Reorder the terms:
9565 = 65 + -5x + x2

Solving
9565 = 65 + -5x + x2

Solving for variable 'x'.

Combine like terms: 9565 + -65 = 9500
9500 + 5x + -1x2 = 65 + -5x + x2 + -65 + 5x + -1x2

Reorder the terms:
9500 + 5x + -1x2 = 65 + -65 + -5x + 5x + x2 + -1x2

Combine like terms: 65 + -65 = 0
9500 + 5x + -1x2 = 0 + -5x + 5x + x2 + -1x2
9500 + 5x + -1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
9500 + 5x + -1x2 = 0 + x2 + -1x2
9500 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9500 + 5x + -1x2 = 0

Factor a trinomial.
(100 + -1x)(95 + x) = 0

Subproblem 1

Set the factor '(100 + -1x)' equal to zero and attempt to solve: Simplifying 100 + -1x = 0 Solving 100 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + -1x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -1x = 0 + -100 -1x = 0 + -100 Combine like terms: 0 + -100 = -100 -1x = -100 Divide each side by '-1'. x = 100 Simplifying x = 100

Subproblem 2

Set the factor '(95 + x)' equal to zero and attempt to solve: Simplifying 95 + x = 0 Solving 95 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-95' to each side of the equation. 95 + -95 + x = 0 + -95 Combine like terms: 95 + -95 = 0 0 + x = 0 + -95 x = 0 + -95 Combine like terms: 0 + -95 = -95 x = -95 Simplifying x = -95

Solution

x = {100, -95}

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