4x^2-17x+23=2x+2

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Solution for 4x^2-17x+23=2x+2 equation:


Simplifying
4x2 + -17x + 23 = 2x + 2

Reorder the terms:
23 + -17x + 4x2 = 2x + 2

Reorder the terms:
23 + -17x + 4x2 = 2 + 2x

Solving
23 + -17x + 4x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
23 + -2 + -17x + -2x + 4x2 = 2 + 2x + -2 + -2x

Combine like terms: 23 + -2 = 21
21 + -17x + -2x + 4x2 = 2 + 2x + -2 + -2x

Combine like terms: -17x + -2x = -19x
21 + -19x + 4x2 = 2 + 2x + -2 + -2x

Reorder the terms:
21 + -19x + 4x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
21 + -19x + 4x2 = 0 + 2x + -2x
21 + -19x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
21 + -19x + 4x2 = 0

Factor a trinomial.
(7 + -4x)(3 + -1x) = 0

Subproblem 1

Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75

Subproblem 2

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

Solution

x = {1.75, 3}

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