2x^2-7x+4=x^2-8

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Solution for 2x^2-7x+4=x^2-8 equation:


Simplifying
2x2 + -7x + 4 = x2 + -8

Reorder the terms:
4 + -7x + 2x2 = x2 + -8

Reorder the terms:
4 + -7x + 2x2 = -8 + x2

Solving
4 + -7x + 2x2 = -8 + x2

Solving for variable 'x'.

Reorder the terms:
4 + 8 + -7x + 2x2 + -1x2 = -8 + x2 + 8 + -1x2

Combine like terms: 4 + 8 = 12
12 + -7x + 2x2 + -1x2 = -8 + x2 + 8 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
12 + -7x + 1x2 = -8 + x2 + 8 + -1x2

Reorder the terms:
12 + -7x + 1x2 = -8 + 8 + x2 + -1x2

Combine like terms: -8 + 8 = 0
12 + -7x + 1x2 = 0 + x2 + -1x2
12 + -7x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -7x + 1x2 = 0

Factor a trinomial.
(3 + -1x)(4 + -1x) = 0

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

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 = {3, 4}

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