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Simplifying x2 + 28x + 56 = 0 Reorder the terms: 56 + 28x + x2 = 0 Solving 56 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + 28x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + 28x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + 28x + x2 = 0 + -56 28x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 28x + x2 = -56 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 = -56 + 196 Reorder the terms: 196 + 28x + x2 = -56 + 196 Combine like terms: -56 + 196 = 140 196 + 28x + x2 = 140 Factor a perfect square on the left side: (x + 14)(x + 14) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (x + 14) equal to 11.832159566 and -11.832159566.Subproblem 1
x + 14 = 11.832159566 Simplifying x + 14 = 11.832159566 Reorder the terms: 14 + x = 11.832159566 Solving 14 + x = 11.832159566 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 = 11.832159566 + -14 Combine like terms: 14 + -14 = 0 0 + x = 11.832159566 + -14 x = 11.832159566 + -14 Combine like terms: 11.832159566 + -14 = -2.167840434 x = -2.167840434 Simplifying x = -2.167840434Subproblem 2
x + 14 = -11.832159566 Simplifying x + 14 = -11.832159566 Reorder the terms: 14 + x = -11.832159566 Solving 14 + x = -11.832159566 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 = -11.832159566 + -14 Combine like terms: 14 + -14 = 0 0 + x = -11.832159566 + -14 x = -11.832159566 + -14 Combine like terms: -11.832159566 + -14 = -25.832159566 x = -25.832159566 Simplifying x = -25.832159566Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.167840434, -25.832159566}
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