4x^2+7x=3x-2

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Solution for 4x^2+7x=3x-2 equation:


Simplifying
4x2 + 7x = 3x + -2

Reorder the terms:
7x + 4x2 = 3x + -2

Reorder the terms:
7x + 4x2 = -2 + 3x

Solving
7x + 4x2 = -2 + 3x

Solving for variable 'x'.

Reorder the terms:
2 + 7x + -3x + 4x2 = -2 + 3x + 2 + -3x

Combine like terms: 7x + -3x = 4x
2 + 4x + 4x2 = -2 + 3x + 2 + -3x

Reorder the terms:
2 + 4x + 4x2 = -2 + 2 + 3x + -3x

Combine like terms: -2 + 2 = 0
2 + 4x + 4x2 = 0 + 3x + -3x
2 + 4x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
2 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 2x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 2x + 2x2 = 0 Solving 1 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x + x2 = 0 + -0.5 x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 x + x2 = -0.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -0.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 1.25 + x2 = -0.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.25 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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