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Simplifying 2x2 + -12x = 36 + 7x Reorder the terms: -12x + 2x2 = 36 + 7x Solving -12x + 2x2 = 36 + 7x Solving for variable 'x'. Reorder the terms: -36 + -12x + -7x + 2x2 = 36 + 7x + -36 + -7x Combine like terms: -12x + -7x = -19x -36 + -19x + 2x2 = 36 + 7x + -36 + -7x Reorder the terms: -36 + -19x + 2x2 = 36 + -36 + 7x + -7x Combine like terms: 36 + -36 = 0 -36 + -19x + 2x2 = 0 + 7x + -7x -36 + -19x + 2x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -36 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18 + -9.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -9.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -9.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -9.5x + x2 = 0 + 18 -9.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -9.5x + x2 = 18 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 18 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 18 + 22.5625 Combine like terms: 18 + 22.5625 = 40.5625 22.5625 + -9.5x + x2 = 40.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 40.5625 Calculate the square root of the right side: 6.368869601 Break this problem into two subproblems by setting (x + -4.75) equal to 6.368869601 and -6.368869601.Subproblem 1
x + -4.75 = 6.368869601 Simplifying x + -4.75 = 6.368869601 Reorder the terms: -4.75 + x = 6.368869601 Solving -4.75 + x = 6.368869601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 6.368869601 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 6.368869601 + 4.75 x = 6.368869601 + 4.75 Combine like terms: 6.368869601 + 4.75 = 11.118869601 x = 11.118869601 Simplifying x = 11.118869601Subproblem 2
x + -4.75 = -6.368869601 Simplifying x + -4.75 = -6.368869601 Reorder the terms: -4.75 + x = -6.368869601 Solving -4.75 + x = -6.368869601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -6.368869601 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -6.368869601 + 4.75 x = -6.368869601 + 4.75 Combine like terms: -6.368869601 + 4.75 = -1.618869601 x = -1.618869601 Simplifying x = -1.618869601Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.118869601, -1.618869601}
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