4x^2-15x+37=9x+2

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Solution for 4x^2-15x+37=9x+2 equation:


Simplifying
4x2 + -15x + 37 = 9x + 2

Reorder the terms:
37 + -15x + 4x2 = 9x + 2

Reorder the terms:
37 + -15x + 4x2 = 2 + 9x

Solving
37 + -15x + 4x2 = 2 + 9x

Solving for variable 'x'.

Reorder the terms:
37 + -2 + -15x + -9x + 4x2 = 2 + 9x + -2 + -9x

Combine like terms: 37 + -2 = 35
35 + -15x + -9x + 4x2 = 2 + 9x + -2 + -9x

Combine like terms: -15x + -9x = -24x
35 + -24x + 4x2 = 2 + 9x + -2 + -9x

Reorder the terms:
35 + -24x + 4x2 = 2 + -2 + 9x + -9x

Combine like terms: 2 + -2 = 0
35 + -24x + 4x2 = 0 + 9x + -9x
35 + -24x + 4x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
35 + -24x + 4x2 = 0

Factor a trinomial.
(5 + -2x)(7 + -2x) = 0

Subproblem 1

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Subproblem 2

Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 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 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5

Solution

x = {2.5, 3.5}

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