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Simplifying 16x2 + -13x + -224 = 0 Reorder the terms: -224 + -13x + 16x2 = 0 Solving -224 + -13x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -14 + -0.8125x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -0.8125x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -0.8125x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -0.8125x + x2 = 0 + 14 -0.8125x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -0.8125x + x2 = 14 The x term is -0.8125x. Take half its coefficient (-0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. -0.8125x + 0.1650390625 + x2 = 14 + 0.1650390625 Reorder the terms: 0.1650390625 + -0.8125x + x2 = 14 + 0.1650390625 Combine like terms: 14 + 0.1650390625 = 14.1650390625 0.1650390625 + -0.8125x + x2 = 14.1650390625 Factor a perfect square on the left side: (x + -0.40625)(x + -0.40625) = 14.1650390625 Calculate the square root of the right side: 3.763647043 Break this problem into two subproblems by setting (x + -0.40625) equal to 3.763647043 and -3.763647043.Subproblem 1
x + -0.40625 = 3.763647043 Simplifying x + -0.40625 = 3.763647043 Reorder the terms: -0.40625 + x = 3.763647043 Solving -0.40625 + x = 3.763647043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + x = 3.763647043 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + x = 3.763647043 + 0.40625 x = 3.763647043 + 0.40625 Combine like terms: 3.763647043 + 0.40625 = 4.169897043 x = 4.169897043 Simplifying x = 4.169897043Subproblem 2
x + -0.40625 = -3.763647043 Simplifying x + -0.40625 = -3.763647043 Reorder the terms: -0.40625 + x = -3.763647043 Solving -0.40625 + x = -3.763647043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + x = -3.763647043 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + x = -3.763647043 + 0.40625 x = -3.763647043 + 0.40625 Combine like terms: -3.763647043 + 0.40625 = -3.357397043 x = -3.357397043 Simplifying x = -3.357397043Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.169897043, -3.357397043}
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