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Simplifying 4x2 + 12x2 + -1x + -3 = 0 Reorder the terms: -3 + -1x + 4x2 + 12x2 = 0 Combine like terms: 4x2 + 12x2 = 16x2 -3 + -1x + 16x2 = 0 Solving -3 + -1x + 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'. -0.1875 + -0.0625x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -0.0625x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -0.0625x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -0.0625x + x2 = 0 + 0.1875 -0.0625x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -0.0625x + x2 = 0.1875 The x term is -0.0625x. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625x + 0.0009765625 + x2 = 0.1875 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625x + x2 = 0.1875 + 0.0009765625 Combine like terms: 0.1875 + 0.0009765625 = 0.1884765625 0.0009765625 + -0.0625x + x2 = 0.1884765625 Factor a perfect square on the left side: (x + -0.03125)(x + -0.03125) = 0.1884765625 Calculate the square root of the right side: 0.434138875 Break this problem into two subproblems by setting (x + -0.03125) equal to 0.434138875 and -0.434138875.Subproblem 1
x + -0.03125 = 0.434138875 Simplifying x + -0.03125 = 0.434138875 Reorder the terms: -0.03125 + x = 0.434138875 Solving -0.03125 + x = 0.434138875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = 0.434138875 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = 0.434138875 + 0.03125 x = 0.434138875 + 0.03125 Combine like terms: 0.434138875 + 0.03125 = 0.465388875 x = 0.465388875 Simplifying x = 0.465388875Subproblem 2
x + -0.03125 = -0.434138875 Simplifying x + -0.03125 = -0.434138875 Reorder the terms: -0.03125 + x = -0.434138875 Solving -0.03125 + x = -0.434138875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = -0.434138875 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = -0.434138875 + 0.03125 x = -0.434138875 + 0.03125 Combine like terms: -0.434138875 + 0.03125 = -0.402888875 x = -0.402888875 Simplifying x = -0.402888875Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.465388875, -0.402888875}
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