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Simplifying 6x2 + 19x + 76x = 2 Reorder the terms: 19x + 76x + 6x2 = 2 Combine like terms: 19x + 76x = 95x 95x + 6x2 = 2 Solving 95x + 6x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 95x + 6x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 95x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.3333333333 + 15.83333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 15.83333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 15.83333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 15.83333333x + x2 = 0 + 0.3333333333 15.83333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 15.83333333x + x2 = 0.3333333333 The x term is 15.83333333x. Take half its coefficient (7.916666665). Square it (62.67361108) and add it to both sides. Add '62.67361108' to each side of the equation. 15.83333333x + 62.67361108 + x2 = 0.3333333333 + 62.67361108 Reorder the terms: 62.67361108 + 15.83333333x + x2 = 0.3333333333 + 62.67361108 Combine like terms: 0.3333333333 + 62.67361108 = 63.0069444133 62.67361108 + 15.83333333x + x2 = 63.0069444133 Factor a perfect square on the left side: (x + 7.916666665)(x + 7.916666665) = 63.0069444133 Calculate the square root of the right side: 7.937691378 Break this problem into two subproblems by setting (x + 7.916666665) equal to 7.937691378 and -7.937691378.Subproblem 1
x + 7.916666665 = 7.937691378 Simplifying x + 7.916666665 = 7.937691378 Reorder the terms: 7.916666665 + x = 7.937691378 Solving 7.916666665 + x = 7.937691378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.916666665' to each side of the equation. 7.916666665 + -7.916666665 + x = 7.937691378 + -7.916666665 Combine like terms: 7.916666665 + -7.916666665 = 0.000000000 0.000000000 + x = 7.937691378 + -7.916666665 x = 7.937691378 + -7.916666665 Combine like terms: 7.937691378 + -7.916666665 = 0.021024713 x = 0.021024713 Simplifying x = 0.021024713Subproblem 2
x + 7.916666665 = -7.937691378 Simplifying x + 7.916666665 = -7.937691378 Reorder the terms: 7.916666665 + x = -7.937691378 Solving 7.916666665 + x = -7.937691378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.916666665' to each side of the equation. 7.916666665 + -7.916666665 + x = -7.937691378 + -7.916666665 Combine like terms: 7.916666665 + -7.916666665 = 0.000000000 0.000000000 + x = -7.937691378 + -7.916666665 x = -7.937691378 + -7.916666665 Combine like terms: -7.937691378 + -7.916666665 = -15.854358043 x = -15.854358043 Simplifying x = -15.854358043Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.021024713, -15.854358043}
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