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Simplifying 16x2 + -21x + -3.5 = 0 Reorder the terms: -3.5 + -21x + 16x2 = 0 Solving -3.5 + -21x + 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'. -0.21875 + -1.3125x + x2 = 0 Move the constant term to the right: Add '0.21875' to each side of the equation. -0.21875 + -1.3125x + 0.21875 + x2 = 0 + 0.21875 Reorder the terms: -0.21875 + 0.21875 + -1.3125x + x2 = 0 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + -1.3125x + x2 = 0 + 0.21875 -1.3125x + x2 = 0 + 0.21875 Combine like terms: 0 + 0.21875 = 0.21875 -1.3125x + x2 = 0.21875 The x term is -1.3125x. Take half its coefficient (-0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. -1.3125x + 0.4306640625 + x2 = 0.21875 + 0.4306640625 Reorder the terms: 0.4306640625 + -1.3125x + x2 = 0.21875 + 0.4306640625 Combine like terms: 0.21875 + 0.4306640625 = 0.6494140625 0.4306640625 + -1.3125x + x2 = 0.6494140625 Factor a perfect square on the left side: (x + -0.65625)(x + -0.65625) = 0.6494140625 Calculate the square root of the right side: 0.80586231 Break this problem into two subproblems by setting (x + -0.65625) equal to 0.80586231 and -0.80586231.Subproblem 1
x + -0.65625 = 0.80586231 Simplifying x + -0.65625 = 0.80586231 Reorder the terms: -0.65625 + x = 0.80586231 Solving -0.65625 + x = 0.80586231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + x = 0.80586231 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + x = 0.80586231 + 0.65625 x = 0.80586231 + 0.65625 Combine like terms: 0.80586231 + 0.65625 = 1.46211231 x = 1.46211231 Simplifying x = 1.46211231Subproblem 2
x + -0.65625 = -0.80586231 Simplifying x + -0.65625 = -0.80586231 Reorder the terms: -0.65625 + x = -0.80586231 Solving -0.65625 + x = -0.80586231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + x = -0.80586231 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + x = -0.80586231 + 0.65625 x = -0.80586231 + 0.65625 Combine like terms: -0.80586231 + 0.65625 = -0.14961231 x = -0.14961231 Simplifying x = -0.14961231Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.46211231, -0.14961231}
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