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Simplifying 6x(3x + 4) = 2 Reorder the terms: 6x(4 + 3x) = 2 (4 * 6x + 3x * 6x) = 2 (24x + 18x2) = 2 Solving 24x + 18x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 24x + 18x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 24x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 12x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 12x + 9x2)' equal to zero and attempt to solve: Simplifying -1 + 12x + 9x2 = 0 Solving -1 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.1111111111 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 1.333333333x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 1.333333333x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + 0.1111111111 1.333333333x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 1.333333333x + x2 = 0.1111111111 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 = 0.1111111111 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.1111111111 + 0.4444444442 Combine like terms: 0.1111111111 + 0.4444444442 = 0.5555555553 0.4444444442 + 1.333333333x + x2 = 0.5555555553 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.5555555553 Calculate the square root of the right side: 0.745355992 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.745355992 and -0.745355992.Subproblem 1
x + 0.6666666665 = 0.745355992 Simplifying x + 0.6666666665 = 0.745355992 Reorder the terms: 0.6666666665 + x = 0.745355992 Solving 0.6666666665 + x = 0.745355992 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 = 0.745355992 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.745355992 + -0.6666666665 x = 0.745355992 + -0.6666666665 Combine like terms: 0.745355992 + -0.6666666665 = 0.0786893255 x = 0.0786893255 Simplifying x = 0.0786893255Subproblem 2
x + 0.6666666665 = -0.745355992 Simplifying x + 0.6666666665 = -0.745355992 Reorder the terms: 0.6666666665 + x = -0.745355992 Solving 0.6666666665 + x = -0.745355992 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 = -0.745355992 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.745355992 + -0.6666666665 x = -0.745355992 + -0.6666666665 Combine like terms: -0.745355992 + -0.6666666665 = -1.4120226585 x = -1.4120226585 Simplifying x = -1.4120226585Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0786893255, -1.4120226585}Solution
x = {0.0786893255, -1.4120226585}
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