(4x+1)-(2x^2+7x+4)=

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Solution for (4x+1)-(2x^2+7x+4)= equation:


Simplifying
(4x + 1) + -1(2x2 + 7x + 4) = 0

Reorder the terms:
(1 + 4x) + -1(2x2 + 7x + 4) = 0

Remove parenthesis around (1 + 4x)
1 + 4x + -1(2x2 + 7x + 4) = 0

Reorder the terms:
1 + 4x + -1(4 + 7x + 2x2) = 0
1 + 4x + (4 * -1 + 7x * -1 + 2x2 * -1) = 0
1 + 4x + (-4 + -7x + -2x2) = 0

Reorder the terms:
1 + -4 + 4x + -7x + -2x2 = 0

Combine like terms: 1 + -4 = -3
-3 + 4x + -7x + -2x2 = 0

Combine like terms: 4x + -7x = -3x
-3 + -3x + -2x2 = 0

Solving
-3 + -3x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 3x + 2x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(3 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + 3x + 2x2 = 0 Solving 3 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.5x + x2 = 0 + -1.5 1.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.5x + x2 = -1.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -1.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -1.5 + 0.5625 Combine like terms: -1.5 + 0.5625 = -0.9375 0.5625 + 1.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -0.9375 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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