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Simplifying 2x2 + 28x + 103 = 30 Reorder the terms: 103 + 28x + 2x2 = 30 Solving 103 + 28x + 2x2 = 30 Solving for variable 'x'. Reorder the terms: 103 + -30 + 28x + 2x2 = 30 + -30 Combine like terms: 103 + -30 = 73 73 + 28x + 2x2 = 30 + -30 Combine like terms: 30 + -30 = 0 73 + 28x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 36.5 + 14x + x2 = 0 Move the constant term to the right: Add '-36.5' to each side of the equation. 36.5 + 14x + -36.5 + x2 = 0 + -36.5 Reorder the terms: 36.5 + -36.5 + 14x + x2 = 0 + -36.5 Combine like terms: 36.5 + -36.5 = 0.0 0.0 + 14x + x2 = 0 + -36.5 14x + x2 = 0 + -36.5 Combine like terms: 0 + -36.5 = -36.5 14x + x2 = -36.5 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -36.5 + 49 Reorder the terms: 49 + 14x + x2 = -36.5 + 49 Combine like terms: -36.5 + 49 = 12.5 49 + 14x + x2 = 12.5 Factor a perfect square on the left side: (x + 7)(x + 7) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + 7) equal to 3.535533906 and -3.535533906.Subproblem 1
x + 7 = 3.535533906 Simplifying x + 7 = 3.535533906 Reorder the terms: 7 + x = 3.535533906 Solving 7 + x = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 3.535533906 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.535533906 + -7 x = 3.535533906 + -7 Combine like terms: 3.535533906 + -7 = -3.464466094 x = -3.464466094 Simplifying x = -3.464466094Subproblem 2
x + 7 = -3.535533906 Simplifying x + 7 = -3.535533906 Reorder the terms: 7 + x = -3.535533906 Solving 7 + x = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -3.535533906 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.535533906 + -7 x = -3.535533906 + -7 Combine like terms: -3.535533906 + -7 = -10.535533906 x = -10.535533906 Simplifying x = -10.535533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.464466094, -10.535533906}
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