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Simplifying 3x2 + -12x = 14 Reorder the terms: -12x + 3x2 = 14 Solving -12x + 3x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + -12x + 3x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.666666667 + -4x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -4x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -4x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + 4.666666667 -4x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -4x + x2 = 4.666666667 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 = 4.666666667 + 4 Reorder the terms: 4 + -4x + x2 = 4.666666667 + 4 Combine like terms: 4.666666667 + 4 = 8.666666667 4 + -4x + x2 = 8.666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 8.666666667 Calculate the square root of the right side: 2.943920289 Break this problem into two subproblems by setting (x + -2) equal to 2.943920289 and -2.943920289.Subproblem 1
x + -2 = 2.943920289 Simplifying x + -2 = 2.943920289 Reorder the terms: -2 + x = 2.943920289 Solving -2 + x = 2.943920289 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 = 2.943920289 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.943920289 + 2 x = 2.943920289 + 2 Combine like terms: 2.943920289 + 2 = 4.943920289 x = 4.943920289 Simplifying x = 4.943920289Subproblem 2
x + -2 = -2.943920289 Simplifying x + -2 = -2.943920289 Reorder the terms: -2 + x = -2.943920289 Solving -2 + x = -2.943920289 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 = -2.943920289 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.943920289 + 2 x = -2.943920289 + 2 Combine like terms: -2.943920289 + 2 = -0.943920289 x = -0.943920289 Simplifying x = -0.943920289Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.943920289, -0.943920289}
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