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Simplifying 4x2 + 128x + -3875 = 0 Reorder the terms: -3875 + 128x + 4x2 = 0 Solving -3875 + 128x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -968.75 + 32x + x2 = 0 Move the constant term to the right: Add '968.75' to each side of the equation. -968.75 + 32x + 968.75 + x2 = 0 + 968.75 Reorder the terms: -968.75 + 968.75 + 32x + x2 = 0 + 968.75 Combine like terms: -968.75 + 968.75 = 0.00 0.00 + 32x + x2 = 0 + 968.75 32x + x2 = 0 + 968.75 Combine like terms: 0 + 968.75 = 968.75 32x + x2 = 968.75 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 968.75 + 256 Reorder the terms: 256 + 32x + x2 = 968.75 + 256 Combine like terms: 968.75 + 256 = 1224.75 256 + 32x + x2 = 1224.75 Factor a perfect square on the left side: (x + 16)(x + 16) = 1224.75 Calculate the square root of the right side: 34.996428389 Break this problem into two subproblems by setting (x + 16) equal to 34.996428389 and -34.996428389.Subproblem 1
x + 16 = 34.996428389 Simplifying x + 16 = 34.996428389 Reorder the terms: 16 + x = 34.996428389 Solving 16 + x = 34.996428389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 34.996428389 + -16 Combine like terms: 16 + -16 = 0 0 + x = 34.996428389 + -16 x = 34.996428389 + -16 Combine like terms: 34.996428389 + -16 = 18.996428389 x = 18.996428389 Simplifying x = 18.996428389Subproblem 2
x + 16 = -34.996428389 Simplifying x + 16 = -34.996428389 Reorder the terms: 16 + x = -34.996428389 Solving 16 + x = -34.996428389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -34.996428389 + -16 Combine like terms: 16 + -16 = 0 0 + x = -34.996428389 + -16 x = -34.996428389 + -16 Combine like terms: -34.996428389 + -16 = -50.996428389 x = -50.996428389 Simplifying x = -50.996428389Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.996428389, -50.996428389}
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