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Simplifying 8x2 + 49x + 56 = 0 Reorder the terms: 56 + 49x + 8x2 = 0 Solving 56 + 49x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 7 + 6.125x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6.125x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 6.125x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6.125x + x2 = 0 + -7 6.125x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 6.125x + x2 = -7 The x term is 6.125x. Take half its coefficient (3.0625). Square it (9.37890625) and add it to both sides. Add '9.37890625' to each side of the equation. 6.125x + 9.37890625 + x2 = -7 + 9.37890625 Reorder the terms: 9.37890625 + 6.125x + x2 = -7 + 9.37890625 Combine like terms: -7 + 9.37890625 = 2.37890625 9.37890625 + 6.125x + x2 = 2.37890625 Factor a perfect square on the left side: (x + 3.0625)(x + 3.0625) = 2.37890625 Calculate the square root of the right side: 1.542370335 Break this problem into two subproblems by setting (x + 3.0625) equal to 1.542370335 and -1.542370335.Subproblem 1
x + 3.0625 = 1.542370335 Simplifying x + 3.0625 = 1.542370335 Reorder the terms: 3.0625 + x = 1.542370335 Solving 3.0625 + x = 1.542370335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.0625' to each side of the equation. 3.0625 + -3.0625 + x = 1.542370335 + -3.0625 Combine like terms: 3.0625 + -3.0625 = 0.0000 0.0000 + x = 1.542370335 + -3.0625 x = 1.542370335 + -3.0625 Combine like terms: 1.542370335 + -3.0625 = -1.520129665 x = -1.520129665 Simplifying x = -1.520129665Subproblem 2
x + 3.0625 = -1.542370335 Simplifying x + 3.0625 = -1.542370335 Reorder the terms: 3.0625 + x = -1.542370335 Solving 3.0625 + x = -1.542370335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.0625' to each side of the equation. 3.0625 + -3.0625 + x = -1.542370335 + -3.0625 Combine like terms: 3.0625 + -3.0625 = 0.0000 0.0000 + x = -1.542370335 + -3.0625 x = -1.542370335 + -3.0625 Combine like terms: -1.542370335 + -3.0625 = -4.604870335 x = -4.604870335 Simplifying x = -4.604870335Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.520129665, -4.604870335}
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