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Simplifying (x2 + -4x + 4) + -4(12x + 9x2) = 0 Reorder the terms: (4 + -4x + x2) + -4(12x + 9x2) = 0 Remove parenthesis around (4 + -4x + x2) 4 + -4x + x2 + -4(12x + 9x2) = 0 4 + -4x + x2 + (12x * -4 + 9x2 * -4) = 0 4 + -4x + x2 + (-48x + -36x2) = 0 Reorder the terms: 4 + -4x + -48x + x2 + -36x2 = 0 Combine like terms: -4x + -48x = -52x 4 + -52x + x2 + -36x2 = 0 Combine like terms: x2 + -36x2 = -35x2 4 + -52x + -35x2 = 0 Solving 4 + -52x + -35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -0.1142857143 + 1.485714286x + x2 = 0 Move the constant term to the right: Add '0.1142857143' to each side of the equation. -0.1142857143 + 1.485714286x + 0.1142857143 + x2 = 0 + 0.1142857143 Reorder the terms: -0.1142857143 + 0.1142857143 + 1.485714286x + x2 = 0 + 0.1142857143 Combine like terms: -0.1142857143 + 0.1142857143 = 0.0000000000 0.0000000000 + 1.485714286x + x2 = 0 + 0.1142857143 1.485714286x + x2 = 0 + 0.1142857143 Combine like terms: 0 + 0.1142857143 = 0.1142857143 1.485714286x + x2 = 0.1142857143 The x term is 1.485714286x. Take half its coefficient (0.742857143). Square it (0.5518367349) and add it to both sides. Add '0.5518367349' to each side of the equation. 1.485714286x + 0.5518367349 + x2 = 0.1142857143 + 0.5518367349 Reorder the terms: 0.5518367349 + 1.485714286x + x2 = 0.1142857143 + 0.5518367349 Combine like terms: 0.1142857143 + 0.5518367349 = 0.6661224492 0.5518367349 + 1.485714286x + x2 = 0.6661224492 Factor a perfect square on the left side: (x + 0.742857143)(x + 0.742857143) = 0.6661224492 Calculate the square root of the right side: 0.816163249 Break this problem into two subproblems by setting (x + 0.742857143) equal to 0.816163249 and -0.816163249.Subproblem 1
x + 0.742857143 = 0.816163249 Simplifying x + 0.742857143 = 0.816163249 Reorder the terms: 0.742857143 + x = 0.816163249 Solving 0.742857143 + x = 0.816163249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.742857143' to each side of the equation. 0.742857143 + -0.742857143 + x = 0.816163249 + -0.742857143 Combine like terms: 0.742857143 + -0.742857143 = 0.000000000 0.000000000 + x = 0.816163249 + -0.742857143 x = 0.816163249 + -0.742857143 Combine like terms: 0.816163249 + -0.742857143 = 0.073306106 x = 0.073306106 Simplifying x = 0.073306106Subproblem 2
x + 0.742857143 = -0.816163249 Simplifying x + 0.742857143 = -0.816163249 Reorder the terms: 0.742857143 + x = -0.816163249 Solving 0.742857143 + x = -0.816163249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.742857143' to each side of the equation. 0.742857143 + -0.742857143 + x = -0.816163249 + -0.742857143 Combine like terms: 0.742857143 + -0.742857143 = 0.000000000 0.000000000 + x = -0.816163249 + -0.742857143 x = -0.816163249 + -0.742857143 Combine like terms: -0.816163249 + -0.742857143 = -1.559020392 x = -1.559020392 Simplifying x = -1.559020392Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.073306106, -1.559020392}
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