x+3(-9)-x+2(2)=4x^2+12x+24

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Solution for x+3(-9)-x+2(2)=4x^2+12x+24 equation:


Simplifying
x + 3(-9) + -1x + 2(2) = 4x2 + 12x + 24

Multiply 3 * -9
x + -27 + -1x + 2(2) = 4x2 + 12x + 24

Multiply 2 * 2
x + -27 + -1x + 4 = 4x2 + 12x + 24

Reorder the terms:
-27 + 4 + x + -1x = 4x2 + 12x + 24

Combine like terms: -27 + 4 = -23
-23 + x + -1x = 4x2 + 12x + 24

Combine like terms: x + -1x = 0
-23 + 0 = 4x2 + 12x + 24
-23 = 4x2 + 12x + 24

Reorder the terms:
-23 = 24 + 12x + 4x2

Solving
-23 = 24 + 12x + 4x2

Solving for variable 'x'.

Combine like terms: -23 + -24 = -47
-47 + -12x + -4x2 = 24 + 12x + 4x2 + -24 + -12x + -4x2

Reorder the terms:
-47 + -12x + -4x2 = 24 + -24 + 12x + -12x + 4x2 + -4x2

Combine like terms: 24 + -24 = 0
-47 + -12x + -4x2 = 0 + 12x + -12x + 4x2 + -4x2
-47 + -12x + -4x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
-47 + -12x + -4x2 = 0 + 4x2 + -4x2
-47 + -12x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-47 + -12x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(47 + 12x + 4x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(47 + 12x + 4x2)' equal to zero and attempt to solve: Simplifying 47 + 12x + 4x2 = 0 Solving 47 + 12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11.75 + 3x + x2 = 0 Move the constant term to the right: Add '-11.75' to each side of the equation. 11.75 + 3x + -11.75 + x2 = 0 + -11.75 Reorder the terms: 11.75 + -11.75 + 3x + x2 = 0 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + 3x + x2 = 0 + -11.75 3x + x2 = 0 + -11.75 Combine like terms: 0 + -11.75 = -11.75 3x + x2 = -11.75 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -11.75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -11.75 + 2.25 Combine like terms: -11.75 + 2.25 = -9.5 2.25 + 3x + x2 = -9.5 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -9.5 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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