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Simplifying 2x2 + 16x + 7 = 0 Reorder the terms: 7 + 16x + 2x2 = 0 Solving 7 + 16x + 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'. 3.5 + 8x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 8x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 8x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 8x + x2 = 0 + -3.5 8x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 8x + x2 = -3.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -3.5 + 16 Reorder the terms: 16 + 8x + x2 = -3.5 + 16 Combine like terms: -3.5 + 16 = 12.5 16 + 8x + x2 = 12.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + 4) equal to 3.535533906 and -3.535533906.Subproblem 1
x + 4 = 3.535533906 Simplifying x + 4 = 3.535533906 Reorder the terms: 4 + x = 3.535533906 Solving 4 + x = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.535533906 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.535533906 + -4 x = 3.535533906 + -4 Combine like terms: 3.535533906 + -4 = -0.464466094 x = -0.464466094 Simplifying x = -0.464466094Subproblem 2
x + 4 = -3.535533906 Simplifying x + 4 = -3.535533906 Reorder the terms: 4 + x = -3.535533906 Solving 4 + x = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.535533906 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.535533906 + -4 x = -3.535533906 + -4 Combine like terms: -3.535533906 + -4 = -7.535533906 x = -7.535533906 Simplifying x = -7.535533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.464466094, -7.535533906}
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