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Simplifying 4x2 + 3x = 120 Reorder the terms: 3x + 4x2 = 120 Solving 3x + 4x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 3x + 4x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -30 + 0.75x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 0.75x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 0.75x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 0.75x + x2 = 0 + 30 0.75x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 0.75x + x2 = 30 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 = 30 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 30 + 0.140625 Combine like terms: 30 + 0.140625 = 30.140625 0.140625 + 0.75x + x2 = 30.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 30.140625 Calculate the square root of the right side: 5.490047814 Break this problem into two subproblems by setting (x + 0.375) equal to 5.490047814 and -5.490047814.Subproblem 1
x + 0.375 = 5.490047814 Simplifying x + 0.375 = 5.490047814 Reorder the terms: 0.375 + x = 5.490047814 Solving 0.375 + x = 5.490047814 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 = 5.490047814 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 5.490047814 + -0.375 x = 5.490047814 + -0.375 Combine like terms: 5.490047814 + -0.375 = 5.115047814 x = 5.115047814 Simplifying x = 5.115047814Subproblem 2
x + 0.375 = -5.490047814 Simplifying x + 0.375 = -5.490047814 Reorder the terms: 0.375 + x = -5.490047814 Solving 0.375 + x = -5.490047814 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 = -5.490047814 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -5.490047814 + -0.375 x = -5.490047814 + -0.375 Combine like terms: -5.490047814 + -0.375 = -5.865047814 x = -5.865047814 Simplifying x = -5.865047814Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.115047814, -5.865047814}
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