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Simplifying 4x2 + 22x + 5 = 0 Reorder the terms: 5 + 22x + 4x2 = 0 Solving 5 + 22x + 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'. 1.25 + 5.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 5.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 5.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 5.5x + x2 = 0 + -1.25 5.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 5.5x + x2 = -1.25 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -1.25 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -1.25 + 7.5625 Combine like terms: -1.25 + 7.5625 = 6.3125 7.5625 + 5.5x + x2 = 6.3125 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 6.3125 Calculate the square root of the right side: 2.512468905 Break this problem into two subproblems by setting (x + 2.75) equal to 2.512468905 and -2.512468905.Subproblem 1
x + 2.75 = 2.512468905 Simplifying x + 2.75 = 2.512468905 Reorder the terms: 2.75 + x = 2.512468905 Solving 2.75 + x = 2.512468905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 2.512468905 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 2.512468905 + -2.75 x = 2.512468905 + -2.75 Combine like terms: 2.512468905 + -2.75 = -0.237531095 x = -0.237531095 Simplifying x = -0.237531095Subproblem 2
x + 2.75 = -2.512468905 Simplifying x + 2.75 = -2.512468905 Reorder the terms: 2.75 + x = -2.512468905 Solving 2.75 + x = -2.512468905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -2.512468905 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -2.512468905 + -2.75 x = -2.512468905 + -2.75 Combine like terms: -2.512468905 + -2.75 = -5.262468905 x = -5.262468905 Simplifying x = -5.262468905Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.237531095, -5.262468905}
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