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Simplifying 0 = 16x2 + 13x + -5 Reorder the terms: 0 = -5 + 13x + 16x2 Solving 0 = -5 + 13x + 16x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + -13x + -16x2 = -5 + 13x + 16x2 + 5 + -13x + -16x2 Reorder the terms: 5 + -13x + -16x2 = -5 + 5 + 13x + -13x + 16x2 + -16x2 Combine like terms: -5 + 5 = 0 5 + -13x + -16x2 = 0 + 13x + -13x + 16x2 + -16x2 5 + -13x + -16x2 = 13x + -13x + 16x2 + -16x2 Combine like terms: 13x + -13x = 0 5 + -13x + -16x2 = 0 + 16x2 + -16x2 5 + -13x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 5 + -13x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + 0.8125x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + 0.8125x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + 0.8125x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + 0.8125x + x2 = 0 + 0.3125 0.8125x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 0.8125x + x2 = 0.3125 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 = 0.3125 + 0.1650390625 Reorder the terms: 0.1650390625 + 0.8125x + x2 = 0.3125 + 0.1650390625 Combine like terms: 0.3125 + 0.1650390625 = 0.4775390625 0.1650390625 + 0.8125x + x2 = 0.4775390625 Factor a perfect square on the left side: (x + 0.40625)(x + 0.40625) = 0.4775390625 Calculate the square root of the right side: 0.691042012 Break this problem into two subproblems by setting (x + 0.40625) equal to 0.691042012 and -0.691042012.Subproblem 1
x + 0.40625 = 0.691042012 Simplifying x + 0.40625 = 0.691042012 Reorder the terms: 0.40625 + x = 0.691042012 Solving 0.40625 + x = 0.691042012 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 = 0.691042012 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + x = 0.691042012 + -0.40625 x = 0.691042012 + -0.40625 Combine like terms: 0.691042012 + -0.40625 = 0.284792012 x = 0.284792012 Simplifying x = 0.284792012Subproblem 2
x + 0.40625 = -0.691042012 Simplifying x + 0.40625 = -0.691042012 Reorder the terms: 0.40625 + x = -0.691042012 Solving 0.40625 + x = -0.691042012 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 = -0.691042012 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + x = -0.691042012 + -0.40625 x = -0.691042012 + -0.40625 Combine like terms: -0.691042012 + -0.40625 = -1.097292012 x = -1.097292012 Simplifying x = -1.097292012Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.284792012, -1.097292012}
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