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Simplifying -1 = 3x2 + -12x Reorder the terms: -1 = -12x + 3x2 Solving -1 = -12x + 3x2 Solving for variable 'x'. Reorder the terms: -1 + 12x + -3x2 = -12x + 12x + 3x2 + -3x2 Combine like terms: -12x + 12x = 0 -1 + 12x + -3x2 = 0 + 3x2 + -3x2 -1 + 12x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -1 + 12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.3333333333 + -4x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -4x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -4x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.3333333333 -4x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -4x + x2 = -0.3333333333 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 = -0.3333333333 + 4 Reorder the terms: 4 + -4x + x2 = -0.3333333333 + 4 Combine like terms: -0.3333333333 + 4 = 3.6666666667 4 + -4x + x2 = 3.6666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.6666666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (x + -2) equal to 1.914854216 and -1.914854216.Subproblem 1
x + -2 = 1.914854216 Simplifying x + -2 = 1.914854216 Reorder the terms: -2 + x = 1.914854216 Solving -2 + x = 1.914854216 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 = 1.914854216 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.914854216 + 2 x = 1.914854216 + 2 Combine like terms: 1.914854216 + 2 = 3.914854216 x = 3.914854216 Simplifying x = 3.914854216Subproblem 2
x + -2 = -1.914854216 Simplifying x + -2 = -1.914854216 Reorder the terms: -2 + x = -1.914854216 Solving -2 + x = -1.914854216 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 = -1.914854216 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.914854216 + 2 x = -1.914854216 + 2 Combine like terms: -1.914854216 + 2 = 0.085145784 x = 0.085145784 Simplifying x = 0.085145784Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.914854216, 0.085145784}
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