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Simplifying x2 + -70x + -680 = 0 Reorder the terms: -680 + -70x + x2 = 0 Solving -680 + -70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '680' to each side of the equation. -680 + -70x + 680 + x2 = 0 + 680 Reorder the terms: -680 + 680 + -70x + x2 = 0 + 680 Combine like terms: -680 + 680 = 0 0 + -70x + x2 = 0 + 680 -70x + x2 = 0 + 680 Combine like terms: 0 + 680 = 680 -70x + x2 = 680 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = 680 + 1225 Reorder the terms: 1225 + -70x + x2 = 680 + 1225 Combine like terms: 680 + 1225 = 1905 1225 + -70x + x2 = 1905 Factor a perfect square on the left side: (x + -35)(x + -35) = 1905 Calculate the square root of the right side: 43.646305686 Break this problem into two subproblems by setting (x + -35) equal to 43.646305686 and -43.646305686.Subproblem 1
x + -35 = 43.646305686 Simplifying x + -35 = 43.646305686 Reorder the terms: -35 + x = 43.646305686 Solving -35 + x = 43.646305686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 43.646305686 + 35 Combine like terms: -35 + 35 = 0 0 + x = 43.646305686 + 35 x = 43.646305686 + 35 Combine like terms: 43.646305686 + 35 = 78.646305686 x = 78.646305686 Simplifying x = 78.646305686Subproblem 2
x + -35 = -43.646305686 Simplifying x + -35 = -43.646305686 Reorder the terms: -35 + x = -43.646305686 Solving -35 + x = -43.646305686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -43.646305686 + 35 Combine like terms: -35 + 35 = 0 0 + x = -43.646305686 + 35 x = -43.646305686 + 35 Combine like terms: -43.646305686 + 35 = -8.646305686 x = -8.646305686 Simplifying x = -8.646305686Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.646305686, -8.646305686}
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