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Simplifying 2x(4x + 7) + -3 = 0 Reorder the terms: 2x(7 + 4x) + -3 = 0 (7 * 2x + 4x * 2x) + -3 = 0 (14x + 8x2) + -3 = 0 Reorder the terms: -3 + 14x + 8x2 = 0 Solving -3 + 14x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + 1.75x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 1.75x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 1.75x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 1.75x + x2 = 0 + 0.375 1.75x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 1.75x + x2 = 0.375 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 0.375 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 0.375 + 0.765625 Combine like terms: 0.375 + 0.765625 = 1.140625 0.765625 + 1.75x + x2 = 1.140625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + 0.875) equal to 1.068000468 and -1.068000468.Subproblem 1
x + 0.875 = 1.068000468 Simplifying x + 0.875 = 1.068000468 Reorder the terms: 0.875 + x = 1.068000468 Solving 0.875 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.068000468 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.068000468 + -0.875 x = 1.068000468 + -0.875 Combine like terms: 1.068000468 + -0.875 = 0.193000468 x = 0.193000468 Simplifying x = 0.193000468Subproblem 2
x + 0.875 = -1.068000468 Simplifying x + 0.875 = -1.068000468 Reorder the terms: 0.875 + x = -1.068000468 Solving 0.875 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.068000468 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.068000468 + -0.875 x = -1.068000468 + -0.875 Combine like terms: -1.068000468 + -0.875 = -1.943000468 x = -1.943000468 Simplifying x = -1.943000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.193000468, -1.943000468}
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