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Simplifying x2 + 62x + 720 = 0 Reorder the terms: 720 + 62x + x2 = 0 Solving 720 + 62x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-720' to each side of the equation. 720 + 62x + -720 + x2 = 0 + -720 Reorder the terms: 720 + -720 + 62x + x2 = 0 + -720 Combine like terms: 720 + -720 = 0 0 + 62x + x2 = 0 + -720 62x + x2 = 0 + -720 Combine like terms: 0 + -720 = -720 62x + x2 = -720 The x term is 62x. Take half its coefficient (31). Square it (961) and add it to both sides. Add '961' to each side of the equation. 62x + 961 + x2 = -720 + 961 Reorder the terms: 961 + 62x + x2 = -720 + 961 Combine like terms: -720 + 961 = 241 961 + 62x + x2 = 241 Factor a perfect square on the left side: (x + 31)(x + 31) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (x + 31) equal to 15.524174696 and -15.524174696.Subproblem 1
x + 31 = 15.524174696 Simplifying x + 31 = 15.524174696 Reorder the terms: 31 + x = 15.524174696 Solving 31 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = 15.524174696 + -31 Combine like terms: 31 + -31 = 0 0 + x = 15.524174696 + -31 x = 15.524174696 + -31 Combine like terms: 15.524174696 + -31 = -15.475825304 x = -15.475825304 Simplifying x = -15.475825304Subproblem 2
x + 31 = -15.524174696 Simplifying x + 31 = -15.524174696 Reorder the terms: 31 + x = -15.524174696 Solving 31 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = -15.524174696 + -31 Combine like terms: 31 + -31 = 0 0 + x = -15.524174696 + -31 x = -15.524174696 + -31 Combine like terms: -15.524174696 + -31 = -46.524174696 x = -46.524174696 Simplifying x = -46.524174696Solution
The solution to the problem is based on the solutions from the subproblems. x = {-15.475825304, -46.524174696}
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