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Simplifying 40x + -1x2 + 39 = 0 Reorder the terms: 39 + 40x + -1x2 = 0 Solving 39 + 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'. -39 + -40x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + -40x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -40x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -40x + x2 = 0 + 39 -40x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -40x + x2 = 39 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 = 39 + 400 Reorder the terms: 400 + -40x + x2 = 39 + 400 Combine like terms: 39 + 400 = 439 400 + -40x + x2 = 439 Factor a perfect square on the left side: (x + -20)(x + -20) = 439 Calculate the square root of the right side: 20.95232684 Break this problem into two subproblems by setting (x + -20) equal to 20.95232684 and -20.95232684.Subproblem 1
x + -20 = 20.95232684 Simplifying x + -20 = 20.95232684 Reorder the terms: -20 + x = 20.95232684 Solving -20 + x = 20.95232684 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 = 20.95232684 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.95232684 + 20 x = 20.95232684 + 20 Combine like terms: 20.95232684 + 20 = 40.95232684 x = 40.95232684 Simplifying x = 40.95232684Subproblem 2
x + -20 = -20.95232684 Simplifying x + -20 = -20.95232684 Reorder the terms: -20 + x = -20.95232684 Solving -20 + x = -20.95232684 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 = -20.95232684 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.95232684 + 20 x = -20.95232684 + 20 Combine like terms: -20.95232684 + 20 = -0.95232684 x = -0.95232684 Simplifying x = -0.95232684Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.95232684, -0.95232684}
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