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Simplifying 684x + 3775(x + -36) * x = 7 Reorder the terms: 684x + 3775(-36 + x) * x = 7 Reorder the terms for easier multiplication: 684x + 3775x(-36 + x) = 7 684x + (-36 * 3775x + x * 3775x) = 7 684x + (-135900x + 3775x2) = 7 Combine like terms: 684x + -135900x = -135216x -135216x + 3775x2 = 7 Solving -135216x + 3775x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -135216x + 3775x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -135216x + 3775x2 = 0 Begin completing the square. Divide all terms by 3775 the coefficient of the squared term: Divide each side by '3775'. -0.001854304636 + -35.81880795x + x2 = 0 Move the constant term to the right: Add '0.001854304636' to each side of the equation. -0.001854304636 + -35.81880795x + 0.001854304636 + x2 = 0 + 0.001854304636 Reorder the terms: -0.001854304636 + 0.001854304636 + -35.81880795x + x2 = 0 + 0.001854304636 Combine like terms: -0.001854304636 + 0.001854304636 = 0.000000000000 0.000000000000 + -35.81880795x + x2 = 0 + 0.001854304636 -35.81880795x + x2 = 0 + 0.001854304636 Combine like terms: 0 + 0.001854304636 = 0.001854304636 -35.81880795x + x2 = 0.001854304636 The x term is -35.81880795x. Take half its coefficient (-17.90940398). Square it (320.7467509) and add it to both sides. Add '320.7467509' to each side of the equation. -35.81880795x + 320.7467509 + x2 = 0.001854304636 + 320.7467509 Reorder the terms: 320.7467509 + -35.81880795x + x2 = 0.001854304636 + 320.7467509 Combine like terms: 0.001854304636 + 320.7467509 = 320.748605204636 320.7467509 + -35.81880795x + x2 = 320.748605204636 Factor a perfect square on the left side: (x + -17.90940398)(x + -17.90940398) = 320.748605204636 Calculate the square root of the right side: 17.909455748 Break this problem into two subproblems by setting (x + -17.90940398) equal to 17.909455748 and -17.909455748.Subproblem 1
x + -17.90940398 = 17.909455748 Simplifying x + -17.90940398 = 17.909455748 Reorder the terms: -17.90940398 + x = 17.909455748 Solving -17.90940398 + x = 17.909455748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.90940398' to each side of the equation. -17.90940398 + 17.90940398 + x = 17.909455748 + 17.90940398 Combine like terms: -17.90940398 + 17.90940398 = 0.00000000 0.00000000 + x = 17.909455748 + 17.90940398 x = 17.909455748 + 17.90940398 Combine like terms: 17.909455748 + 17.90940398 = 35.818859728 x = 35.818859728 Simplifying x = 35.818859728Subproblem 2
x + -17.90940398 = -17.909455748 Simplifying x + -17.90940398 = -17.909455748 Reorder the terms: -17.90940398 + x = -17.909455748 Solving -17.90940398 + x = -17.909455748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.90940398' to each side of the equation. -17.90940398 + 17.90940398 + x = -17.909455748 + 17.90940398 Combine like terms: -17.90940398 + 17.90940398 = 0.00000000 0.00000000 + x = -17.909455748 + 17.90940398 x = -17.909455748 + 17.90940398 Combine like terms: -17.909455748 + 17.90940398 = -0.000051768 x = -0.000051768 Simplifying x = -0.000051768Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.818859728, -0.000051768}
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