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Simplifying 16x2 + 65.5x + 5.5 = 0 Reorder the terms: 5.5 + 65.5x + 16x2 = 0 Solving 5.5 + 65.5x + 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'. 0.34375 + 4.09375x + x2 = 0 Move the constant term to the right: Add '-0.34375' to each side of the equation. 0.34375 + 4.09375x + -0.34375 + x2 = 0 + -0.34375 Reorder the terms: 0.34375 + -0.34375 + 4.09375x + x2 = 0 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + 4.09375x + x2 = 0 + -0.34375 4.09375x + x2 = 0 + -0.34375 Combine like terms: 0 + -0.34375 = -0.34375 4.09375x + x2 = -0.34375 The x term is 4.09375x. Take half its coefficient (2.046875). Square it (4.189697266) and add it to both sides. Add '4.189697266' to each side of the equation. 4.09375x + 4.189697266 + x2 = -0.34375 + 4.189697266 Reorder the terms: 4.189697266 + 4.09375x + x2 = -0.34375 + 4.189697266 Combine like terms: -0.34375 + 4.189697266 = 3.845947266 4.189697266 + 4.09375x + x2 = 3.845947266 Factor a perfect square on the left side: (x + 2.046875)(x + 2.046875) = 3.845947266 Calculate the square root of the right side: 1.961108683 Break this problem into two subproblems by setting (x + 2.046875) equal to 1.961108683 and -1.961108683.Subproblem 1
x + 2.046875 = 1.961108683 Simplifying x + 2.046875 = 1.961108683 Reorder the terms: 2.046875 + x = 1.961108683 Solving 2.046875 + x = 1.961108683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.046875' to each side of the equation. 2.046875 + -2.046875 + x = 1.961108683 + -2.046875 Combine like terms: 2.046875 + -2.046875 = 0.000000 0.000000 + x = 1.961108683 + -2.046875 x = 1.961108683 + -2.046875 Combine like terms: 1.961108683 + -2.046875 = -0.085766317 x = -0.085766317 Simplifying x = -0.085766317Subproblem 2
x + 2.046875 = -1.961108683 Simplifying x + 2.046875 = -1.961108683 Reorder the terms: 2.046875 + x = -1.961108683 Solving 2.046875 + x = -1.961108683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.046875' to each side of the equation. 2.046875 + -2.046875 + x = -1.961108683 + -2.046875 Combine like terms: 2.046875 + -2.046875 = 0.000000 0.000000 + x = -1.961108683 + -2.046875 x = -1.961108683 + -2.046875 Combine like terms: -1.961108683 + -2.046875 = -4.007983683 x = -4.007983683 Simplifying x = -4.007983683Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.085766317, -4.007983683}
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