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Simplifying 1700 + -40x + -1x2 = 0 Solving 1700 + -40x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1700 + 40x + x2 = 0 Move the constant term to the right: Add '1700' to each side of the equation. -1700 + 40x + 1700 + x2 = 0 + 1700 Reorder the terms: -1700 + 1700 + 40x + x2 = 0 + 1700 Combine like terms: -1700 + 1700 = 0 0 + 40x + x2 = 0 + 1700 40x + x2 = 0 + 1700 Combine like terms: 0 + 1700 = 1700 40x + x2 = 1700 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 1700 + 400 Reorder the terms: 400 + 40x + x2 = 1700 + 400 Combine like terms: 1700 + 400 = 2100 400 + 40x + x2 = 2100 Factor a perfect square on the left side: (x + 20)(x + 20) = 2100 Calculate the square root of the right side: 45.82575695 Break this problem into two subproblems by setting (x + 20) equal to 45.82575695 and -45.82575695.Subproblem 1
x + 20 = 45.82575695 Simplifying x + 20 = 45.82575695 Reorder the terms: 20 + x = 45.82575695 Solving 20 + x = 45.82575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 45.82575695 + -20 Combine like terms: 20 + -20 = 0 0 + x = 45.82575695 + -20 x = 45.82575695 + -20 Combine like terms: 45.82575695 + -20 = 25.82575695 x = 25.82575695 Simplifying x = 25.82575695Subproblem 2
x + 20 = -45.82575695 Simplifying x + 20 = -45.82575695 Reorder the terms: 20 + x = -45.82575695 Solving 20 + x = -45.82575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -45.82575695 + -20 Combine like terms: 20 + -20 = 0 0 + x = -45.82575695 + -20 x = -45.82575695 + -20 Combine like terms: -45.82575695 + -20 = -65.82575695 x = -65.82575695 Simplifying x = -65.82575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.82575695, -65.82575695}
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