x^2-3x+4.5=8.5

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Solution for x^2-3x+4.5=8.5 equation:


Simplifying
x2 + -3x + 4.5 = 8.5

Reorder the terms:
4.5 + -3x + x2 = 8.5

Solving
4.5 + -3x + x2 = 8.5

Solving for variable 'x'.

Reorder the terms:
4.5 + -8.5 + -3x + x2 = 8.5 + -8.5

Combine like terms: 4.5 + -8.5 = -4
-4 + -3x + x2 = 8.5 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
-4 + -3x + x2 = 0.0

Factor a trinomial.
(-1 + -1x)(4 + -1x) = 0.0

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-1, 4}

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