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Simplifying 12 + x = -3x(4 + -1x) 12 + x = (4 * -3x + -1x * -3x) 12 + x = (-12x + 3x2) Solving 12 + x = -12x + 3x2 Solving for variable 'x'. Combine like terms: x + 12x = 13x 12 + 13x + -3x2 = -12x + 3x2 + 12x + -3x2 Reorder the terms: 12 + 13x + -3x2 = -12x + 12x + 3x2 + -3x2 Combine like terms: -12x + 12x = 0 12 + 13x + -3x2 = 0 + 3x2 + -3x2 12 + 13x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 12 + 13x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4.333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -4.333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4.333333333x + x2 = 0 + 4 -4.333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4.333333333x + x2 = 4 The x term is -4.333333333x. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333x + 4.694444446 + x2 = 4 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = 4 + 4.694444446 Combine like terms: 4 + 4.694444446 = 8.694444446 4.694444446 + -4.333333333x + x2 = 8.694444446 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 8.694444446 Calculate the square root of the right side: 2.948634336 Break this problem into two subproblems by setting (x + -2.166666667) equal to 2.948634336 and -2.948634336.Subproblem 1
x + -2.166666667 = 2.948634336 Simplifying x + -2.166666667 = 2.948634336 Reorder the terms: -2.166666667 + x = 2.948634336 Solving -2.166666667 + x = 2.948634336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 2.948634336 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 2.948634336 + 2.166666667 x = 2.948634336 + 2.166666667 Combine like terms: 2.948634336 + 2.166666667 = 5.115301003 x = 5.115301003 Simplifying x = 5.115301003Subproblem 2
x + -2.166666667 = -2.948634336 Simplifying x + -2.166666667 = -2.948634336 Reorder the terms: -2.166666667 + x = -2.948634336 Solving -2.166666667 + x = -2.948634336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -2.948634336 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -2.948634336 + 2.166666667 x = -2.948634336 + 2.166666667 Combine like terms: -2.948634336 + 2.166666667 = -0.781967669 x = -0.781967669 Simplifying x = -0.781967669Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.115301003, -0.781967669}
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