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Simplifying 4x2 + -37x + -14 = 0 Reorder the terms: -14 + -37x + 4x2 = 0 Solving -14 + -37x + 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'. -3.5 + -9.25x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -9.25x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -9.25x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -9.25x + x2 = 0 + 3.5 -9.25x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -9.25x + x2 = 3.5 The x term is -9.25x. Take half its coefficient (-4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. -9.25x + 21.390625 + x2 = 3.5 + 21.390625 Reorder the terms: 21.390625 + -9.25x + x2 = 3.5 + 21.390625 Combine like terms: 3.5 + 21.390625 = 24.890625 21.390625 + -9.25x + x2 = 24.890625 Factor a perfect square on the left side: (x + -4.625)(x + -4.625) = 24.890625 Calculate the square root of the right side: 4.989050511 Break this problem into two subproblems by setting (x + -4.625) equal to 4.989050511 and -4.989050511.Subproblem 1
x + -4.625 = 4.989050511 Simplifying x + -4.625 = 4.989050511 Reorder the terms: -4.625 + x = 4.989050511 Solving -4.625 + x = 4.989050511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = 4.989050511 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = 4.989050511 + 4.625 x = 4.989050511 + 4.625 Combine like terms: 4.989050511 + 4.625 = 9.614050511 x = 9.614050511 Simplifying x = 9.614050511Subproblem 2
x + -4.625 = -4.989050511 Simplifying x + -4.625 = -4.989050511 Reorder the terms: -4.625 + x = -4.989050511 Solving -4.625 + x = -4.989050511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = -4.989050511 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = -4.989050511 + 4.625 x = -4.989050511 + 4.625 Combine like terms: -4.989050511 + 4.625 = -0.364050511 x = -0.364050511 Simplifying x = -0.364050511Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.614050511, -0.364050511}
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