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Simplifying 7x + 2 = 12x2 + 4x + -8 Reorder the terms: 2 + 7x = 12x2 + 4x + -8 Reorder the terms: 2 + 7x = -8 + 4x + 12x2 Solving 2 + 7x = -8 + 4x + 12x2 Solving for variable 'x'. Reorder the terms: 2 + 8 + 7x + -4x + -12x2 = -8 + 4x + 12x2 + 8 + -4x + -12x2 Combine like terms: 2 + 8 = 10 10 + 7x + -4x + -12x2 = -8 + 4x + 12x2 + 8 + -4x + -12x2 Combine like terms: 7x + -4x = 3x 10 + 3x + -12x2 = -8 + 4x + 12x2 + 8 + -4x + -12x2 Reorder the terms: 10 + 3x + -12x2 = -8 + 8 + 4x + -4x + 12x2 + -12x2 Combine like terms: -8 + 8 = 0 10 + 3x + -12x2 = 0 + 4x + -4x + 12x2 + -12x2 10 + 3x + -12x2 = 4x + -4x + 12x2 + -12x2 Combine like terms: 4x + -4x = 0 10 + 3x + -12x2 = 0 + 12x2 + -12x2 10 + 3x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 10 + 3x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.8333333333 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -0.25x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -0.25x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -0.25x + x2 = 0 + 0.8333333333 -0.25x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -0.25x + x2 = 0.8333333333 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.8333333333 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.8333333333 + 0.015625 Combine like terms: 0.8333333333 + 0.015625 = 0.8489583333 0.015625 + -0.25x + x2 = 0.8489583333 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.8489583333 Calculate the square root of the right side: 0.921389349 Break this problem into two subproblems by setting (x + -0.125) equal to 0.921389349 and -0.921389349.Subproblem 1
x + -0.125 = 0.921389349 Simplifying x + -0.125 = 0.921389349 Reorder the terms: -0.125 + x = 0.921389349 Solving -0.125 + x = 0.921389349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.921389349 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.921389349 + 0.125 x = 0.921389349 + 0.125 Combine like terms: 0.921389349 + 0.125 = 1.046389349 x = 1.046389349 Simplifying x = 1.046389349Subproblem 2
x + -0.125 = -0.921389349 Simplifying x + -0.125 = -0.921389349 Reorder the terms: -0.125 + x = -0.921389349 Solving -0.125 + x = -0.921389349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.921389349 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.921389349 + 0.125 x = -0.921389349 + 0.125 Combine like terms: -0.921389349 + 0.125 = -0.796389349 x = -0.796389349 Simplifying x = -0.796389349Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.046389349, -0.796389349}
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