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Simplifying x2 + 28x + 58 = 0 Reorder the terms: 58 + 28x + x2 = 0 Solving 58 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + 28x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + 28x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + 28x + x2 = 0 + -58 28x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 28x + x2 = -58 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -58 + 196 Reorder the terms: 196 + 28x + x2 = -58 + 196 Combine like terms: -58 + 196 = 138 196 + 28x + x2 = 138 Factor a perfect square on the left side: (x + 14)(x + 14) = 138 Calculate the square root of the right side: 11.747340124 Break this problem into two subproblems by setting (x + 14) equal to 11.747340124 and -11.747340124.Subproblem 1
x + 14 = 11.747340124 Simplifying x + 14 = 11.747340124 Reorder the terms: 14 + x = 11.747340124 Solving 14 + x = 11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 11.747340124 + -14 Combine like terms: 14 + -14 = 0 0 + x = 11.747340124 + -14 x = 11.747340124 + -14 Combine like terms: 11.747340124 + -14 = -2.252659876 x = -2.252659876 Simplifying x = -2.252659876Subproblem 2
x + 14 = -11.747340124 Simplifying x + 14 = -11.747340124 Reorder the terms: 14 + x = -11.747340124 Solving 14 + x = -11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -11.747340124 + -14 Combine like terms: 14 + -14 = 0 0 + x = -11.747340124 + -14 x = -11.747340124 + -14 Combine like terms: -11.747340124 + -14 = -25.747340124 x = -25.747340124 Simplifying x = -25.747340124Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.252659876, -25.747340124}
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