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Simplifying 12x2 + -48x + 47 = 0 Reorder the terms: 47 + -48x + 12x2 = 0 Solving 47 + -48x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 3.916666667 + -4x + x2 = 0 Move the constant term to the right: Add '-3.916666667' to each side of the equation. 3.916666667 + -4x + -3.916666667 + x2 = 0 + -3.916666667 Reorder the terms: 3.916666667 + -3.916666667 + -4x + x2 = 0 + -3.916666667 Combine like terms: 3.916666667 + -3.916666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + -3.916666667 -4x + x2 = 0 + -3.916666667 Combine like terms: 0 + -3.916666667 = -3.916666667 -4x + x2 = -3.916666667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3.916666667 + 4 Reorder the terms: 4 + -4x + x2 = -3.916666667 + 4 Combine like terms: -3.916666667 + 4 = 0.083333333 4 + -4x + x2 = 0.083333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.083333333 Calculate the square root of the right side: 0.288675134 Break this problem into two subproblems by setting (x + -2) equal to 0.288675134 and -0.288675134.Subproblem 1
x + -2 = 0.288675134 Simplifying x + -2 = 0.288675134 Reorder the terms: -2 + x = 0.288675134 Solving -2 + x = 0.288675134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.288675134 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.288675134 + 2 x = 0.288675134 + 2 Combine like terms: 0.288675134 + 2 = 2.288675134 x = 2.288675134 Simplifying x = 2.288675134Subproblem 2
x + -2 = -0.288675134 Simplifying x + -2 = -0.288675134 Reorder the terms: -2 + x = -0.288675134 Solving -2 + x = -0.288675134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.288675134 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.288675134 + 2 x = -0.288675134 + 2 Combine like terms: -0.288675134 + 2 = 1.711324866 x = 1.711324866 Simplifying x = 1.711324866Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.288675134, 1.711324866}
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