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Simplifying 4x + 5x2 + 12x = 14x2 + -10x + -30 Reorder the terms: 4x + 12x + 5x2 = 14x2 + -10x + -30 Combine like terms: 4x + 12x = 16x 16x + 5x2 = 14x2 + -10x + -30 Reorder the terms: 16x + 5x2 = -30 + -10x + 14x2 Solving 16x + 5x2 = -30 + -10x + 14x2 Solving for variable 'x'. Reorder the terms: 30 + 16x + 10x + 5x2 + -14x2 = -30 + -10x + 14x2 + 30 + 10x + -14x2 Combine like terms: 16x + 10x = 26x 30 + 26x + 5x2 + -14x2 = -30 + -10x + 14x2 + 30 + 10x + -14x2 Combine like terms: 5x2 + -14x2 = -9x2 30 + 26x + -9x2 = -30 + -10x + 14x2 + 30 + 10x + -14x2 Reorder the terms: 30 + 26x + -9x2 = -30 + 30 + -10x + 10x + 14x2 + -14x2 Combine like terms: -30 + 30 = 0 30 + 26x + -9x2 = 0 + -10x + 10x + 14x2 + -14x2 30 + 26x + -9x2 = -10x + 10x + 14x2 + -14x2 Combine like terms: -10x + 10x = 0 30 + 26x + -9x2 = 0 + 14x2 + -14x2 30 + 26x + -9x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 30 + 26x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -3.333333333 + -2.888888889x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -2.888888889x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -2.888888889x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -2.888888889x + x2 = 0 + 3.333333333 -2.888888889x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -2.888888889x + x2 = 3.333333333 The x term is -2.888888889x. Take half its coefficient (-1.444444445). Square it (2.086419755) and add it to both sides. Add '2.086419755' to each side of the equation. -2.888888889x + 2.086419755 + x2 = 3.333333333 + 2.086419755 Reorder the terms: 2.086419755 + -2.888888889x + x2 = 3.333333333 + 2.086419755 Combine like terms: 3.333333333 + 2.086419755 = 5.419753088 2.086419755 + -2.888888889x + x2 = 5.419753088 Factor a perfect square on the left side: (x + -1.444444445)(x + -1.444444445) = 5.419753088 Calculate the square root of the right side: 2.328036316 Break this problem into two subproblems by setting (x + -1.444444445) equal to 2.328036316 and -2.328036316.Subproblem 1
x + -1.444444445 = 2.328036316 Simplifying x + -1.444444445 = 2.328036316 Reorder the terms: -1.444444445 + x = 2.328036316 Solving -1.444444445 + x = 2.328036316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + x = 2.328036316 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = 2.328036316 + 1.444444445 x = 2.328036316 + 1.444444445 Combine like terms: 2.328036316 + 1.444444445 = 3.772480761 x = 3.772480761 Simplifying x = 3.772480761Subproblem 2
x + -1.444444445 = -2.328036316 Simplifying x + -1.444444445 = -2.328036316 Reorder the terms: -1.444444445 + x = -2.328036316 Solving -1.444444445 + x = -2.328036316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + x = -2.328036316 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = -2.328036316 + 1.444444445 x = -2.328036316 + 1.444444445 Combine like terms: -2.328036316 + 1.444444445 = -0.883591871 x = -0.883591871 Simplifying x = -0.883591871Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.772480761, -0.883591871}
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