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Simplifying 4x2 + 5x = 380 Reorder the terms: 5x + 4x2 = 380 Solving 5x + 4x2 = 380 Solving for variable 'x'. Reorder the terms: -380 + 5x + 4x2 = 380 + -380 Combine like terms: 380 + -380 = 0 -380 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -95 + 1.25x + x2 = 0 Move the constant term to the right: Add '95' to each side of the equation. -95 + 1.25x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + 1.25x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + 1.25x + x2 = 0 + 95 1.25x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 1.25x + x2 = 95 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 95 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 95 + 0.390625 Combine like terms: 95 + 0.390625 = 95.390625 0.390625 + 1.25x + x2 = 95.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 95.390625 Calculate the square root of the right side: 9.766812428 Break this problem into two subproblems by setting (x + 0.625) equal to 9.766812428 and -9.766812428.Subproblem 1
x + 0.625 = 9.766812428 Simplifying x + 0.625 = 9.766812428 Reorder the terms: 0.625 + x = 9.766812428 Solving 0.625 + x = 9.766812428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 9.766812428 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 9.766812428 + -0.625 x = 9.766812428 + -0.625 Combine like terms: 9.766812428 + -0.625 = 9.141812428 x = 9.141812428 Simplifying x = 9.141812428Subproblem 2
x + 0.625 = -9.766812428 Simplifying x + 0.625 = -9.766812428 Reorder the terms: 0.625 + x = -9.766812428 Solving 0.625 + x = -9.766812428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -9.766812428 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -9.766812428 + -0.625 x = -9.766812428 + -0.625 Combine like terms: -9.766812428 + -0.625 = -10.391812428 x = -10.391812428 Simplifying x = -10.391812428Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.141812428, -10.391812428}
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