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Simplifying 4x2 + 34x + 47 = 0 Reorder the terms: 47 + 34x + 4x2 = 0 Solving 47 + 34x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11.75 + 8.5x + x2 = 0 Move the constant term to the right: Add '-11.75' to each side of the equation. 11.75 + 8.5x + -11.75 + x2 = 0 + -11.75 Reorder the terms: 11.75 + -11.75 + 8.5x + x2 = 0 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + 8.5x + x2 = 0 + -11.75 8.5x + x2 = 0 + -11.75 Combine like terms: 0 + -11.75 = -11.75 8.5x + x2 = -11.75 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = -11.75 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -11.75 + 18.0625 Combine like terms: -11.75 + 18.0625 = 6.3125 18.0625 + 8.5x + x2 = 6.3125 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 6.3125 Calculate the square root of the right side: 2.512468905 Break this problem into two subproblems by setting (x + 4.25) equal to 2.512468905 and -2.512468905.Subproblem 1
x + 4.25 = 2.512468905 Simplifying x + 4.25 = 2.512468905 Reorder the terms: 4.25 + x = 2.512468905 Solving 4.25 + x = 2.512468905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 2.512468905 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 2.512468905 + -4.25 x = 2.512468905 + -4.25 Combine like terms: 2.512468905 + -4.25 = -1.737531095 x = -1.737531095 Simplifying x = -1.737531095Subproblem 2
x + 4.25 = -2.512468905 Simplifying x + 4.25 = -2.512468905 Reorder the terms: 4.25 + x = -2.512468905 Solving 4.25 + x = -2.512468905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -2.512468905 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -2.512468905 + -4.25 x = -2.512468905 + -4.25 Combine like terms: -2.512468905 + -4.25 = -6.762468905 x = -6.762468905 Simplifying x = -6.762468905Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.737531095, -6.762468905}
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