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Simplifying 4x2 + 3x = 360 Reorder the terms: 3x + 4x2 = 360 Solving 3x + 4x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 3x + 4x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -90 + 0.75x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 0.75x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 0.75x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 0.75x + x2 = 0 + 90 0.75x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 0.75x + x2 = 90 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 = 90 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 90 + 0.140625 Combine like terms: 90 + 0.140625 = 90.140625 0.140625 + 0.75x + x2 = 90.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 90.140625 Calculate the square root of the right side: 9.494241676 Break this problem into two subproblems by setting (x + 0.375) equal to 9.494241676 and -9.494241676.Subproblem 1
x + 0.375 = 9.494241676 Simplifying x + 0.375 = 9.494241676 Reorder the terms: 0.375 + x = 9.494241676 Solving 0.375 + x = 9.494241676 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 = 9.494241676 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 9.494241676 + -0.375 x = 9.494241676 + -0.375 Combine like terms: 9.494241676 + -0.375 = 9.119241676 x = 9.119241676 Simplifying x = 9.119241676Subproblem 2
x + 0.375 = -9.494241676 Simplifying x + 0.375 = -9.494241676 Reorder the terms: 0.375 + x = -9.494241676 Solving 0.375 + x = -9.494241676 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 = -9.494241676 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -9.494241676 + -0.375 x = -9.494241676 + -0.375 Combine like terms: -9.494241676 + -0.375 = -9.869241676 x = -9.869241676 Simplifying x = -9.869241676Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.119241676, -9.869241676}
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