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Simplifying x2 + -7x + -76 = 0 Reorder the terms: -76 + -7x + x2 = 0 Solving -76 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + -7x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + -7x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + -7x + x2 = 0 + 76 -7x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 -7x + x2 = 76 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 76 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 76 + 12.25 Combine like terms: 76 + 12.25 = 88.25 12.25 + -7x + x2 = 88.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (x + -3.5) equal to 9.394147114 and -9.394147114.Subproblem 1
x + -3.5 = 9.394147114 Simplifying x + -3.5 = 9.394147114 Reorder the terms: -3.5 + x = 9.394147114 Solving -3.5 + x = 9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 9.394147114 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 9.394147114 + 3.5 x = 9.394147114 + 3.5 Combine like terms: 9.394147114 + 3.5 = 12.894147114 x = 12.894147114 Simplifying x = 12.894147114Subproblem 2
x + -3.5 = -9.394147114 Simplifying x + -3.5 = -9.394147114 Reorder the terms: -3.5 + x = -9.394147114 Solving -3.5 + x = -9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -9.394147114 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -9.394147114 + 3.5 x = -9.394147114 + 3.5 Combine like terms: -9.394147114 + 3.5 = -5.894147114 x = -5.894147114 Simplifying x = -5.894147114Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.894147114, -5.894147114}
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