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Simplifying (4x + 3)(x) = 320 Reorder the terms: (3 + 4x)(x) = 320 Reorder the terms for easier multiplication: x(3 + 4x) = 320 (3 * x + 4x * x) = 320 (3x + 4x2) = 320 Solving 3x + 4x2 = 320 Solving for variable 'x'. Reorder the terms: -320 + 3x + 4x2 = 320 + -320 Combine like terms: 320 + -320 = 0 -320 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -80 + 0.75x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 0.75x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 0.75x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 0.75x + x2 = 0 + 80 0.75x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 0.75x + x2 = 80 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 80 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 80 + 0.140625 Combine like terms: 80 + 0.140625 = 80.140625 0.140625 + 0.75x + x2 = 80.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 80.140625 Calculate the square root of the right side: 8.952129635 Break this problem into two subproblems by setting (x + 0.375) equal to 8.952129635 and -8.952129635.Subproblem 1
x + 0.375 = 8.952129635 Simplifying x + 0.375 = 8.952129635 Reorder the terms: 0.375 + x = 8.952129635 Solving 0.375 + x = 8.952129635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 8.952129635 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 8.952129635 + -0.375 x = 8.952129635 + -0.375 Combine like terms: 8.952129635 + -0.375 = 8.577129635 x = 8.577129635 Simplifying x = 8.577129635Subproblem 2
x + 0.375 = -8.952129635 Simplifying x + 0.375 = -8.952129635 Reorder the terms: 0.375 + x = -8.952129635 Solving 0.375 + x = -8.952129635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -8.952129635 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -8.952129635 + -0.375 x = -8.952129635 + -0.375 Combine like terms: -8.952129635 + -0.375 = -9.327129635 x = -9.327129635 Simplifying x = -9.327129635Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.577129635, -9.327129635}
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