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Simplifying x2 + -76x + -80 = 0 Reorder the terms: -80 + -76x + x2 = 0 Solving -80 + -76x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -76x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -76x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -76x + x2 = 0 + 80 -76x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -76x + x2 = 80 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 = 80 + 1444 Reorder the terms: 1444 + -76x + x2 = 80 + 1444 Combine like terms: 80 + 1444 = 1524 1444 + -76x + x2 = 1524 Factor a perfect square on the left side: (x + -38)(x + -38) = 1524 Calculate the square root of the right side: 39.038442592 Break this problem into two subproblems by setting (x + -38) equal to 39.038442592 and -39.038442592.Subproblem 1
x + -38 = 39.038442592 Simplifying x + -38 = 39.038442592 Reorder the terms: -38 + x = 39.038442592 Solving -38 + x = 39.038442592 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 = 39.038442592 + 38 Combine like terms: -38 + 38 = 0 0 + x = 39.038442592 + 38 x = 39.038442592 + 38 Combine like terms: 39.038442592 + 38 = 77.038442592 x = 77.038442592 Simplifying x = 77.038442592Subproblem 2
x + -38 = -39.038442592 Simplifying x + -38 = -39.038442592 Reorder the terms: -38 + x = -39.038442592 Solving -38 + x = -39.038442592 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 = -39.038442592 + 38 Combine like terms: -38 + 38 = 0 0 + x = -39.038442592 + 38 x = -39.038442592 + 38 Combine like terms: -39.038442592 + 38 = -1.038442592 x = -1.038442592 Simplifying x = -1.038442592Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.038442592, -1.038442592}
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