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Simplifying 3x + 4x2 = 116 Solving 3x + 4x2 = 116 Solving for variable 'x'. Reorder the terms: -116 + 3x + 4x2 = 116 + -116 Combine like terms: 116 + -116 = 0 -116 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -29 + 0.75x + x2 = 0 Move the constant term to the right: Add '29' to each side of the equation. -29 + 0.75x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 0.75x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 0.75x + x2 = 0 + 29 0.75x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 0.75x + x2 = 29 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 = 29 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 29 + 0.140625 Combine like terms: 29 + 0.140625 = 29.140625 0.140625 + 0.75x + x2 = 29.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 29.140625 Calculate the square root of the right side: 5.39820572 Break this problem into two subproblems by setting (x + 0.375) equal to 5.39820572 and -5.39820572.Subproblem 1
x + 0.375 = 5.39820572 Simplifying x + 0.375 = 5.39820572 Reorder the terms: 0.375 + x = 5.39820572 Solving 0.375 + x = 5.39820572 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 = 5.39820572 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 5.39820572 + -0.375 x = 5.39820572 + -0.375 Combine like terms: 5.39820572 + -0.375 = 5.02320572 x = 5.02320572 Simplifying x = 5.02320572Subproblem 2
x + 0.375 = -5.39820572 Simplifying x + 0.375 = -5.39820572 Reorder the terms: 0.375 + x = -5.39820572 Solving 0.375 + x = -5.39820572 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 = -5.39820572 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -5.39820572 + -0.375 x = -5.39820572 + -0.375 Combine like terms: -5.39820572 + -0.375 = -5.77320572 x = -5.77320572 Simplifying x = -5.77320572Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.02320572, -5.77320572}
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