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Simplifying x2 + 76x + -316 = 0 Reorder the terms: -316 + 76x + x2 = 0 Solving -316 + 76x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '316' to each side of the equation. -316 + 76x + 316 + x2 = 0 + 316 Reorder the terms: -316 + 316 + 76x + x2 = 0 + 316 Combine like terms: -316 + 316 = 0 0 + 76x + x2 = 0 + 316 76x + x2 = 0 + 316 Combine like terms: 0 + 316 = 316 76x + x2 = 316 The x term is 76x. Take half its coefficient (38). Square it (1444) and add it to both sides. Add '1444' to each side of the equation. 76x + 1444 + x2 = 316 + 1444 Reorder the terms: 1444 + 76x + x2 = 316 + 1444 Combine like terms: 316 + 1444 = 1760 1444 + 76x + x2 = 1760 Factor a perfect square on the left side: (x + 38)(x + 38) = 1760 Calculate the square root of the right side: 41.952353927 Break this problem into two subproblems by setting (x + 38) equal to 41.952353927 and -41.952353927.Subproblem 1
x + 38 = 41.952353927 Simplifying x + 38 = 41.952353927 Reorder the terms: 38 + x = 41.952353927 Solving 38 + x = 41.952353927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = 41.952353927 + -38 Combine like terms: 38 + -38 = 0 0 + x = 41.952353927 + -38 x = 41.952353927 + -38 Combine like terms: 41.952353927 + -38 = 3.952353927 x = 3.952353927 Simplifying x = 3.952353927Subproblem 2
x + 38 = -41.952353927 Simplifying x + 38 = -41.952353927 Reorder the terms: 38 + x = -41.952353927 Solving 38 + x = -41.952353927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = -41.952353927 + -38 Combine like terms: 38 + -38 = 0 0 + x = -41.952353927 + -38 x = -41.952353927 + -38 Combine like terms: -41.952353927 + -38 = -79.952353927 x = -79.952353927 Simplifying x = -79.952353927Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.952353927, -79.952353927}
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