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Simplifying x2 + 4x + -59 = -7 Reorder the terms: -59 + 4x + x2 = -7 Solving -59 + 4x + x2 = -7 Solving for variable 'x'. Reorder the terms: -59 + 7 + 4x + x2 = -7 + 7 Combine like terms: -59 + 7 = -52 -52 + 4x + x2 = -7 + 7 Combine like terms: -7 + 7 = 0 -52 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 4x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 4x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 4x + x2 = 0 + 52 4x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 4x + x2 = 52 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 52 + 4 Reorder the terms: 4 + 4x + x2 = 52 + 4 Combine like terms: 52 + 4 = 56 4 + 4x + x2 = 56 Factor a perfect square on the left side: (x + 2)(x + 2) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 2) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 2 = 7.483314774 Simplifying x + 2 = 7.483314774 Reorder the terms: 2 + x = 7.483314774 Solving 2 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 7.483314774 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.483314774 + -2 x = 7.483314774 + -2 Combine like terms: 7.483314774 + -2 = 5.483314774 x = 5.483314774 Simplifying x = 5.483314774Subproblem 2
x + 2 = -7.483314774 Simplifying x + 2 = -7.483314774 Reorder the terms: 2 + x = -7.483314774 Solving 2 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -7.483314774 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.483314774 + -2 x = -7.483314774 + -2 Combine like terms: -7.483314774 + -2 = -9.483314774 x = -9.483314774 Simplifying x = -9.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.483314774, -9.483314774}
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