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Simplifying 4x2 + -9x + 6 + 12x2 + 5x + -13 = 0 Reorder the terms: 6 + -13 + -9x + 5x + 4x2 + 12x2 = 0 Combine like terms: 6 + -13 = -7 -7 + -9x + 5x + 4x2 + 12x2 = 0 Combine like terms: -9x + 5x = -4x -7 + -4x + 4x2 + 12x2 = 0 Combine like terms: 4x2 + 12x2 = 16x2 -7 + -4x + 16x2 = 0 Solving -7 + -4x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -0.25x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -0.25x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -0.25x + x2 = 0 + 0.4375 -0.25x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -0.25x + x2 = 0.4375 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 = 0.4375 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.4375 + 0.015625 Combine like terms: 0.4375 + 0.015625 = 0.453125 0.015625 + -0.25x + x2 = 0.453125 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.453125 Calculate the square root of the right side: 0.673145601 Break this problem into two subproblems by setting (x + -0.125) equal to 0.673145601 and -0.673145601.Subproblem 1
x + -0.125 = 0.673145601 Simplifying x + -0.125 = 0.673145601 Reorder the terms: -0.125 + x = 0.673145601 Solving -0.125 + x = 0.673145601 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 = 0.673145601 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.673145601 + 0.125 x = 0.673145601 + 0.125 Combine like terms: 0.673145601 + 0.125 = 0.798145601 x = 0.798145601 Simplifying x = 0.798145601Subproblem 2
x + -0.125 = -0.673145601 Simplifying x + -0.125 = -0.673145601 Reorder the terms: -0.125 + x = -0.673145601 Solving -0.125 + x = -0.673145601 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 = -0.673145601 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.673145601 + 0.125 x = -0.673145601 + 0.125 Combine like terms: -0.673145601 + 0.125 = -0.548145601 x = -0.548145601 Simplifying x = -0.548145601Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.798145601, -0.548145601}
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