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Simplifying 4x2 + 5x = 440 Reorder the terms: 5x + 4x2 = 440 Solving 5x + 4x2 = 440 Solving for variable 'x'. Reorder the terms: -440 + 5x + 4x2 = 440 + -440 Combine like terms: 440 + -440 = 0 -440 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -110 + 1.25x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + 1.25x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 1.25x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 1.25x + x2 = 0 + 110 1.25x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 1.25x + x2 = 110 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 = 110 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 110 + 0.390625 Combine like terms: 110 + 0.390625 = 110.390625 0.390625 + 1.25x + x2 = 110.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 110.390625 Calculate the square root of the right side: 10.506694295 Break this problem into two subproblems by setting (x + 0.625) equal to 10.506694295 and -10.506694295.Subproblem 1
x + 0.625 = 10.506694295 Simplifying x + 0.625 = 10.506694295 Reorder the terms: 0.625 + x = 10.506694295 Solving 0.625 + x = 10.506694295 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 = 10.506694295 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 10.506694295 + -0.625 x = 10.506694295 + -0.625 Combine like terms: 10.506694295 + -0.625 = 9.881694295 x = 9.881694295 Simplifying x = 9.881694295Subproblem 2
x + 0.625 = -10.506694295 Simplifying x + 0.625 = -10.506694295 Reorder the terms: 0.625 + x = -10.506694295 Solving 0.625 + x = -10.506694295 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 = -10.506694295 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -10.506694295 + -0.625 x = -10.506694295 + -0.625 Combine like terms: -10.506694295 + -0.625 = -11.131694295 x = -11.131694295 Simplifying x = -11.131694295Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.881694295, -11.131694295}
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