-4x^2=5x+9

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Solution for -4x^2=5x+9 equation:


Simplifying
-4x2 = 5x + 9

Reorder the terms:
-4x2 = 9 + 5x

Solving
-4x2 = 9 + 5x

Solving for variable 'x'.

Reorder the terms:
-9 + -5x + -4x2 = 9 + 5x + -9 + -5x

Reorder the terms:
-9 + -5x + -4x2 = 9 + -9 + 5x + -5x

Combine like terms: 9 + -9 = 0
-9 + -5x + -4x2 = 0 + 5x + -5x
-9 + -5x + -4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-9 + -5x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 5x + 4x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(9 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + 5x + 4x2 = 0 Solving 9 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 1.25x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 1.25x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 1.25x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 1.25x + x2 = 0 + -2.25 1.25x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 1.25x + x2 = -2.25 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -2.25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -2.25 + 0.390625 Combine like terms: -2.25 + 0.390625 = -1.859375 0.390625 + 1.25x + x2 = -1.859375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -1.859375 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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