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Simplifying x2 + -4x = 74 Reorder the terms: -4x + x2 = 74 Solving -4x + x2 = 74 Solving for variable 'x'. Reorder the terms: -74 + -4x + x2 = 74 + -74 Combine like terms: 74 + -74 = 0 -74 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -4x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + -4x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -4x + x2 = 0 + 74 -4x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 -4x + x2 = 74 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 74 + 4 Reorder the terms: 4 + -4x + x2 = 74 + 4 Combine like terms: 74 + 4 = 78 4 + -4x + x2 = 78 Factor a perfect square on the left side: (x + -2)(x + -2) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + -2) equal to 8.831760866 and -8.831760866.Subproblem 1
x + -2 = 8.831760866 Simplifying x + -2 = 8.831760866 Reorder the terms: -2 + x = 8.831760866 Solving -2 + x = 8.831760866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 8.831760866 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.831760866 + 2 x = 8.831760866 + 2 Combine like terms: 8.831760866 + 2 = 10.831760866 x = 10.831760866 Simplifying x = 10.831760866Subproblem 2
x + -2 = -8.831760866 Simplifying x + -2 = -8.831760866 Reorder the terms: -2 + x = -8.831760866 Solving -2 + x = -8.831760866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -8.831760866 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.831760866 + 2 x = -8.831760866 + 2 Combine like terms: -8.831760866 + 2 = -6.831760866 x = -6.831760866 Simplifying x = -6.831760866Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.831760866, -6.831760866}
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