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Simplifying 16x2 + 13x + 16 = 81 Reorder the terms: 16 + 13x + 16x2 = 81 Solving 16 + 13x + 16x2 = 81 Solving for variable 'x'. Reorder the terms: 16 + -81 + 13x + 16x2 = 81 + -81 Combine like terms: 16 + -81 = -65 -65 + 13x + 16x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -65 + 13x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -4.0625 + 0.8125x + x2 = 0 Move the constant term to the right: Add '4.0625' to each side of the equation. -4.0625 + 0.8125x + 4.0625 + x2 = 0 + 4.0625 Reorder the terms: -4.0625 + 4.0625 + 0.8125x + x2 = 0 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + 0.8125x + x2 = 0 + 4.0625 0.8125x + x2 = 0 + 4.0625 Combine like terms: 0 + 4.0625 = 4.0625 0.8125x + x2 = 4.0625 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 = 4.0625 + 0.1650390625 Reorder the terms: 0.1650390625 + 0.8125x + x2 = 4.0625 + 0.1650390625 Combine like terms: 4.0625 + 0.1650390625 = 4.2275390625 0.1650390625 + 0.8125x + x2 = 4.2275390625 Factor a perfect square on the left side: (x + 0.40625)(x + 0.40625) = 4.2275390625 Calculate the square root of the right side: 2.056098019 Break this problem into two subproblems by setting (x + 0.40625) equal to 2.056098019 and -2.056098019.Subproblem 1
x + 0.40625 = 2.056098019 Simplifying x + 0.40625 = 2.056098019 Reorder the terms: 0.40625 + x = 2.056098019 Solving 0.40625 + x = 2.056098019 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 = 2.056098019 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + x = 2.056098019 + -0.40625 x = 2.056098019 + -0.40625 Combine like terms: 2.056098019 + -0.40625 = 1.649848019 x = 1.649848019 Simplifying x = 1.649848019Subproblem 2
x + 0.40625 = -2.056098019 Simplifying x + 0.40625 = -2.056098019 Reorder the terms: 0.40625 + x = -2.056098019 Solving 0.40625 + x = -2.056098019 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 = -2.056098019 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + x = -2.056098019 + -0.40625 x = -2.056098019 + -0.40625 Combine like terms: -2.056098019 + -0.40625 = -2.462348019 x = -2.462348019 Simplifying x = -2.462348019Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.649848019, -2.462348019}
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