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Simplifying 4x2 + 3x = 20 Reorder the terms: 3x + 4x2 = 20 Solving 3x + 4x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 3x + 4x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5 + 0.75x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.75x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.75x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.75x + x2 = 0 + 5 0.75x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.75x + x2 = 5 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 = 5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 5 + 0.140625 Combine like terms: 5 + 0.140625 = 5.140625 0.140625 + 0.75x + x2 = 5.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (x + 0.375) equal to 2.267294643 and -2.267294643.Subproblem 1
x + 0.375 = 2.267294643 Simplifying x + 0.375 = 2.267294643 Reorder the terms: 0.375 + x = 2.267294643 Solving 0.375 + x = 2.267294643 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 = 2.267294643 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 2.267294643 + -0.375 x = 2.267294643 + -0.375 Combine like terms: 2.267294643 + -0.375 = 1.892294643 x = 1.892294643 Simplifying x = 1.892294643Subproblem 2
x + 0.375 = -2.267294643 Simplifying x + 0.375 = -2.267294643 Reorder the terms: 0.375 + x = -2.267294643 Solving 0.375 + x = -2.267294643 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 = -2.267294643 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -2.267294643 + -0.375 x = -2.267294643 + -0.375 Combine like terms: -2.267294643 + -0.375 = -2.642294643 x = -2.642294643 Simplifying x = -2.642294643Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.892294643, -2.642294643}
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