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Simplifying 4x2 + 5x = 480 Reorder the terms: 5x + 4x2 = 480 Solving 5x + 4x2 = 480 Solving for variable 'x'. Reorder the terms: -480 + 5x + 4x2 = 480 + -480 Combine like terms: 480 + -480 = 0 -480 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -120 + 1.25x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 1.25x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 1.25x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 1.25x + x2 = 0 + 120 1.25x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 1.25x + x2 = 120 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 = 120 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 120 + 0.390625 Combine like terms: 120 + 0.390625 = 120.390625 0.390625 + 1.25x + x2 = 120.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 120.390625 Calculate the square root of the right side: 10.972266174 Break this problem into two subproblems by setting (x + 0.625) equal to 10.972266174 and -10.972266174.Subproblem 1
x + 0.625 = 10.972266174 Simplifying x + 0.625 = 10.972266174 Reorder the terms: 0.625 + x = 10.972266174 Solving 0.625 + x = 10.972266174 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 = 10.972266174 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 10.972266174 + -0.625 x = 10.972266174 + -0.625 Combine like terms: 10.972266174 + -0.625 = 10.347266174 x = 10.347266174 Simplifying x = 10.347266174Subproblem 2
x + 0.625 = -10.972266174 Simplifying x + 0.625 = -10.972266174 Reorder the terms: 0.625 + x = -10.972266174 Solving 0.625 + x = -10.972266174 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 = -10.972266174 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -10.972266174 + -0.625 x = -10.972266174 + -0.625 Combine like terms: -10.972266174 + -0.625 = -11.597266174 x = -11.597266174 Simplifying x = -11.597266174Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.347266174, -11.597266174}
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