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Simplifying 10 + -6(8x + -2) * 9x + -1(3 + 4x) = 0 Reorder the terms: 10 + -6(-2 + 8x) * 9x + -1(3 + 4x) = 0 Reorder the terms for easier multiplication: 10 + -6 * 9x(-2 + 8x) + -1(3 + 4x) = 0 Multiply -6 * 9 10 + -54x(-2 + 8x) + -1(3 + 4x) = 0 10 + (-2 * -54x + 8x * -54x) + -1(3 + 4x) = 0 10 + (108x + -432x2) + -1(3 + 4x) = 0 10 + 108x + -432x2 + (3 * -1 + 4x * -1) = 0 10 + 108x + -432x2 + (-3 + -4x) = 0 Reorder the terms: 10 + -3 + 108x + -4x + -432x2 = 0 Combine like terms: 10 + -3 = 7 7 + 108x + -4x + -432x2 = 0 Combine like terms: 108x + -4x = 104x 7 + 104x + -432x2 = 0 Solving 7 + 104x + -432x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -432 the coefficient of the squared term: Divide each side by '-432'. -0.0162037037 + -0.2407407407x + x2 = 0 Move the constant term to the right: Add '0.0162037037' to each side of the equation. -0.0162037037 + -0.2407407407x + 0.0162037037 + x2 = 0 + 0.0162037037 Reorder the terms: -0.0162037037 + 0.0162037037 + -0.2407407407x + x2 = 0 + 0.0162037037 Combine like terms: -0.0162037037 + 0.0162037037 = 0.0000000000 0.0000000000 + -0.2407407407x + x2 = 0 + 0.0162037037 -0.2407407407x + x2 = 0 + 0.0162037037 Combine like terms: 0 + 0.0162037037 = 0.0162037037 -0.2407407407x + x2 = 0.0162037037 The x term is -0.2407407407x. Take half its coefficient (-0.1203703704). Square it (0.01448902607) and add it to both sides. Add '0.01448902607' to each side of the equation. -0.2407407407x + 0.01448902607 + x2 = 0.0162037037 + 0.01448902607 Reorder the terms: 0.01448902607 + -0.2407407407x + x2 = 0.0162037037 + 0.01448902607 Combine like terms: 0.0162037037 + 0.01448902607 = 0.03069272977 0.01448902607 + -0.2407407407x + x2 = 0.03069272977 Factor a perfect square on the left side: (x + -0.1203703704)(x + -0.1203703704) = 0.03069272977 Calculate the square root of the right side: 0.175193407 Break this problem into two subproblems by setting (x + -0.1203703704) equal to 0.175193407 and -0.175193407.Subproblem 1
x + -0.1203703704 = 0.175193407 Simplifying x + -0.1203703704 = 0.175193407 Reorder the terms: -0.1203703704 + x = 0.175193407 Solving -0.1203703704 + x = 0.175193407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1203703704' to each side of the equation. -0.1203703704 + 0.1203703704 + x = 0.175193407 + 0.1203703704 Combine like terms: -0.1203703704 + 0.1203703704 = 0.0000000000 0.0000000000 + x = 0.175193407 + 0.1203703704 x = 0.175193407 + 0.1203703704 Combine like terms: 0.175193407 + 0.1203703704 = 0.2955637774 x = 0.2955637774 Simplifying x = 0.2955637774Subproblem 2
x + -0.1203703704 = -0.175193407 Simplifying x + -0.1203703704 = -0.175193407 Reorder the terms: -0.1203703704 + x = -0.175193407 Solving -0.1203703704 + x = -0.175193407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1203703704' to each side of the equation. -0.1203703704 + 0.1203703704 + x = -0.175193407 + 0.1203703704 Combine like terms: -0.1203703704 + 0.1203703704 = 0.0000000000 0.0000000000 + x = -0.175193407 + 0.1203703704 x = -0.175193407 + 0.1203703704 Combine like terms: -0.175193407 + 0.1203703704 = -0.0548230366 x = -0.0548230366 Simplifying x = -0.0548230366Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2955637774, -0.0548230366}
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