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Simplifying 2x2 + 56x + -29 = 0 Reorder the terms: -29 + 56x + 2x2 = 0 Solving -29 + 56x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.5 + 28x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + 28x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + 28x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + 28x + x2 = 0 + 14.5 28x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 28x + x2 = 14.5 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 = 14.5 + 196 Reorder the terms: 196 + 28x + x2 = 14.5 + 196 Combine like terms: 14.5 + 196 = 210.5 196 + 28x + x2 = 210.5 Factor a perfect square on the left side: (x + 14)(x + 14) = 210.5 Calculate the square root of the right side: 14.508618129 Break this problem into two subproblems by setting (x + 14) equal to 14.508618129 and -14.508618129.Subproblem 1
x + 14 = 14.508618129 Simplifying x + 14 = 14.508618129 Reorder the terms: 14 + x = 14.508618129 Solving 14 + x = 14.508618129 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 = 14.508618129 + -14 Combine like terms: 14 + -14 = 0 0 + x = 14.508618129 + -14 x = 14.508618129 + -14 Combine like terms: 14.508618129 + -14 = 0.508618129 x = 0.508618129 Simplifying x = 0.508618129Subproblem 2
x + 14 = -14.508618129 Simplifying x + 14 = -14.508618129 Reorder the terms: 14 + x = -14.508618129 Solving 14 + x = -14.508618129 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 = -14.508618129 + -14 Combine like terms: 14 + -14 = 0 0 + x = -14.508618129 + -14 x = -14.508618129 + -14 Combine like terms: -14.508618129 + -14 = -28.508618129 x = -28.508618129 Simplifying x = -28.508618129Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.508618129, -28.508618129}
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