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Simplifying 6x2 + 8x + -12 = 2x2 + -3x + 6 Reorder the terms: -12 + 8x + 6x2 = 2x2 + -3x + 6 Reorder the terms: -12 + 8x + 6x2 = 6 + -3x + 2x2 Solving -12 + 8x + 6x2 = 6 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: -12 + -6 + 8x + 3x + 6x2 + -2x2 = 6 + -3x + 2x2 + -6 + 3x + -2x2 Combine like terms: -12 + -6 = -18 -18 + 8x + 3x + 6x2 + -2x2 = 6 + -3x + 2x2 + -6 + 3x + -2x2 Combine like terms: 8x + 3x = 11x -18 + 11x + 6x2 + -2x2 = 6 + -3x + 2x2 + -6 + 3x + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 -18 + 11x + 4x2 = 6 + -3x + 2x2 + -6 + 3x + -2x2 Reorder the terms: -18 + 11x + 4x2 = 6 + -6 + -3x + 3x + 2x2 + -2x2 Combine like terms: 6 + -6 = 0 -18 + 11x + 4x2 = 0 + -3x + 3x + 2x2 + -2x2 -18 + 11x + 4x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 -18 + 11x + 4x2 = 0 + 2x2 + -2x2 -18 + 11x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -18 + 11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + 2.75x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 2.75x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 2.75x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 2.75x + x2 = 0 + 4.5 2.75x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 2.75x + x2 = 4.5 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 4.5 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 4.5 + 1.890625 Combine like terms: 4.5 + 1.890625 = 6.390625 1.890625 + 2.75x + x2 = 6.390625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 6.390625 Calculate the square root of the right side: 2.527968552 Break this problem into two subproblems by setting (x + 1.375) equal to 2.527968552 and -2.527968552.Subproblem 1
x + 1.375 = 2.527968552 Simplifying x + 1.375 = 2.527968552 Reorder the terms: 1.375 + x = 2.527968552 Solving 1.375 + x = 2.527968552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 2.527968552 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 2.527968552 + -1.375 x = 2.527968552 + -1.375 Combine like terms: 2.527968552 + -1.375 = 1.152968552 x = 1.152968552 Simplifying x = 1.152968552Subproblem 2
x + 1.375 = -2.527968552 Simplifying x + 1.375 = -2.527968552 Reorder the terms: 1.375 + x = -2.527968552 Solving 1.375 + x = -2.527968552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -2.527968552 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -2.527968552 + -1.375 x = -2.527968552 + -1.375 Combine like terms: -2.527968552 + -1.375 = -3.902968552 x = -3.902968552 Simplifying x = -3.902968552Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.152968552, -3.902968552}
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