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Simplifying (6x2 + -5) + -1(2x2 + 3x + -2) = 0 Reorder the terms: (-5 + 6x2) + -1(2x2 + 3x + -2) = 0 Remove parenthesis around (-5 + 6x2) -5 + 6x2 + -1(2x2 + 3x + -2) = 0 Reorder the terms: -5 + 6x2 + -1(-2 + 3x + 2x2) = 0 -5 + 6x2 + (-2 * -1 + 3x * -1 + 2x2 * -1) = 0 -5 + 6x2 + (2 + -3x + -2x2) = 0 Reorder the terms: -5 + 2 + -3x + 6x2 + -2x2 = 0 Combine like terms: -5 + 2 = -3 -3 + -3x + 6x2 + -2x2 = 0 Combine like terms: 6x2 + -2x2 = 4x2 -3 + -3x + 4x2 = 0 Solving -3 + -3x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -0.75x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.75x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.75x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.75x + x2 = 0 + 0.75 -0.75x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.75x + x2 = 0.75 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 0.75 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 0.75 + 0.140625 Combine like terms: 0.75 + 0.140625 = 0.890625 0.140625 + -0.75x + x2 = 0.890625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + -0.375) equal to 0.943729304 and -0.943729304.Subproblem 1
x + -0.375 = 0.943729304 Simplifying x + -0.375 = 0.943729304 Reorder the terms: -0.375 + x = 0.943729304 Solving -0.375 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.943729304 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.943729304 + 0.375 x = 0.943729304 + 0.375 Combine like terms: 0.943729304 + 0.375 = 1.318729304 x = 1.318729304 Simplifying x = 1.318729304Subproblem 2
x + -0.375 = -0.943729304 Simplifying x + -0.375 = -0.943729304 Reorder the terms: -0.375 + x = -0.943729304 Solving -0.375 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.943729304 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.943729304 + 0.375 x = -0.943729304 + 0.375 Combine like terms: -0.943729304 + 0.375 = -0.568729304 x = -0.568729304 Simplifying x = -0.568729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.318729304, -0.568729304}
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