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Simplifying 66000 = 3x2 + 4x + 2 Reorder the terms: 66000 = 2 + 4x + 3x2 Solving 66000 = 2 + 4x + 3x2 Solving for variable 'x'. Combine like terms: 66000 + -2 = 65998 65998 + -4x + -3x2 = 2 + 4x + 3x2 + -2 + -4x + -3x2 Reorder the terms: 65998 + -4x + -3x2 = 2 + -2 + 4x + -4x + 3x2 + -3x2 Combine like terms: 2 + -2 = 0 65998 + -4x + -3x2 = 0 + 4x + -4x + 3x2 + -3x2 65998 + -4x + -3x2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 65998 + -4x + -3x2 = 0 + 3x2 + -3x2 65998 + -4x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 65998 + -4x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -21999.33333 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '21999.33333' to each side of the equation. -21999.33333 + 1.333333333x + 21999.33333 + x2 = 0 + 21999.33333 Reorder the terms: -21999.33333 + 21999.33333 + 1.333333333x + x2 = 0 + 21999.33333 Combine like terms: -21999.33333 + 21999.33333 = 0.00000 0.00000 + 1.333333333x + x2 = 0 + 21999.33333 1.333333333x + x2 = 0 + 21999.33333 Combine like terms: 0 + 21999.33333 = 21999.33333 1.333333333x + x2 = 21999.33333 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 21999.33333 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 21999.33333 + 0.4444444442 Combine like terms: 21999.33333 + 0.4444444442 = 21999.7777744442 0.4444444442 + 1.333333333x + x2 = 21999.7777744442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 21999.7777744442 Calculate the square root of the right side: 148.323220618 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 148.323220618 and -148.323220618.Subproblem 1
x + 0.6666666665 = 148.323220618 Simplifying x + 0.6666666665 = 148.323220618 Reorder the terms: 0.6666666665 + x = 148.323220618 Solving 0.6666666665 + x = 148.323220618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 148.323220618 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 148.323220618 + -0.6666666665 x = 148.323220618 + -0.6666666665 Combine like terms: 148.323220618 + -0.6666666665 = 147.6565539515 x = 147.6565539515 Simplifying x = 147.6565539515Subproblem 2
x + 0.6666666665 = -148.323220618 Simplifying x + 0.6666666665 = -148.323220618 Reorder the terms: 0.6666666665 + x = -148.323220618 Solving 0.6666666665 + x = -148.323220618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -148.323220618 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -148.323220618 + -0.6666666665 x = -148.323220618 + -0.6666666665 Combine like terms: -148.323220618 + -0.6666666665 = -148.9898872845 x = -148.9898872845 Simplifying x = -148.9898872845Solution
The solution to the problem is based on the solutions from the subproblems. x = {147.6565539515, -148.9898872845}
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