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Simplifying x2 + 4x + 4 + 16x2 + -7 = 0 Reorder the terms: 4 + -7 + 4x + x2 + 16x2 = 0 Combine like terms: 4 + -7 = -3 -3 + 4x + x2 + 16x2 = 0 Combine like terms: x2 + 16x2 = 17x2 -3 + 4x + 17x2 = 0 Solving -3 + 4x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.1764705882 + 0.2352941176x + x2 = 0 Move the constant term to the right: Add '0.1764705882' to each side of the equation. -0.1764705882 + 0.2352941176x + 0.1764705882 + x2 = 0 + 0.1764705882 Reorder the terms: -0.1764705882 + 0.1764705882 + 0.2352941176x + x2 = 0 + 0.1764705882 Combine like terms: -0.1764705882 + 0.1764705882 = 0.0000000000 0.0000000000 + 0.2352941176x + x2 = 0 + 0.1764705882 0.2352941176x + x2 = 0 + 0.1764705882 Combine like terms: 0 + 0.1764705882 = 0.1764705882 0.2352941176x + x2 = 0.1764705882 The x term is 0.2352941176x. Take half its coefficient (0.1176470588). Square it (0.01384083044) and add it to both sides. Add '0.01384083044' to each side of the equation. 0.2352941176x + 0.01384083044 + x2 = 0.1764705882 + 0.01384083044 Reorder the terms: 0.01384083044 + 0.2352941176x + x2 = 0.1764705882 + 0.01384083044 Combine like terms: 0.1764705882 + 0.01384083044 = 0.19031141864 0.01384083044 + 0.2352941176x + x2 = 0.19031141864 Factor a perfect square on the left side: (x + 0.1176470588)(x + 0.1176470588) = 0.19031141864 Calculate the square root of the right side: 0.43624697 Break this problem into two subproblems by setting (x + 0.1176470588) equal to 0.43624697 and -0.43624697.Subproblem 1
x + 0.1176470588 = 0.43624697 Simplifying x + 0.1176470588 = 0.43624697 Reorder the terms: 0.1176470588 + x = 0.43624697 Solving 0.1176470588 + x = 0.43624697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1176470588' to each side of the equation. 0.1176470588 + -0.1176470588 + x = 0.43624697 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + x = 0.43624697 + -0.1176470588 x = 0.43624697 + -0.1176470588 Combine like terms: 0.43624697 + -0.1176470588 = 0.3185999112 x = 0.3185999112 Simplifying x = 0.3185999112Subproblem 2
x + 0.1176470588 = -0.43624697 Simplifying x + 0.1176470588 = -0.43624697 Reorder the terms: 0.1176470588 + x = -0.43624697 Solving 0.1176470588 + x = -0.43624697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1176470588' to each side of the equation. 0.1176470588 + -0.1176470588 + x = -0.43624697 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + x = -0.43624697 + -0.1176470588 x = -0.43624697 + -0.1176470588 Combine like terms: -0.43624697 + -0.1176470588 = -0.5538940288 x = -0.5538940288 Simplifying x = -0.5538940288Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3185999112, -0.5538940288}
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