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Simplifying 7x2 + 56x + 16 = 0 Reorder the terms: 16 + 56x + 7x2 = 0 Solving 16 + 56x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.285714286 + 8x + x2 = 0 Move the constant term to the right: Add '-2.285714286' to each side of the equation. 2.285714286 + 8x + -2.285714286 + x2 = 0 + -2.285714286 Reorder the terms: 2.285714286 + -2.285714286 + 8x + x2 = 0 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + 8x + x2 = 0 + -2.285714286 8x + x2 = 0 + -2.285714286 Combine like terms: 0 + -2.285714286 = -2.285714286 8x + x2 = -2.285714286 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 = -2.285714286 + 16 Reorder the terms: 16 + 8x + x2 = -2.285714286 + 16 Combine like terms: -2.285714286 + 16 = 13.714285714 16 + 8x + x2 = 13.714285714 Factor a perfect square on the left side: (x + 4)(x + 4) = 13.714285714 Calculate the square root of the right side: 3.703280399 Break this problem into two subproblems by setting (x + 4) equal to 3.703280399 and -3.703280399.Subproblem 1
x + 4 = 3.703280399 Simplifying x + 4 = 3.703280399 Reorder the terms: 4 + x = 3.703280399 Solving 4 + x = 3.703280399 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 = 3.703280399 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.703280399 + -4 x = 3.703280399 + -4 Combine like terms: 3.703280399 + -4 = -0.296719601 x = -0.296719601 Simplifying x = -0.296719601Subproblem 2
x + 4 = -3.703280399 Simplifying x + 4 = -3.703280399 Reorder the terms: 4 + x = -3.703280399 Solving 4 + x = -3.703280399 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 = -3.703280399 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.703280399 + -4 x = -3.703280399 + -4 Combine like terms: -3.703280399 + -4 = -7.703280399 x = -7.703280399 Simplifying x = -7.703280399Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.296719601, -7.703280399}
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