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Simplifying -1x2 + 40x + -15 = 0 Reorder the terms: -15 + 40x + -1x2 = 0 Solving -15 + 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'. 15 + -40x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -40x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -40x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -40x + x2 = 0 + -15 -40x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -40x + x2 = -15 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 = -15 + 400 Reorder the terms: 400 + -40x + x2 = -15 + 400 Combine like terms: -15 + 400 = 385 400 + -40x + x2 = 385 Factor a perfect square on the left side: (x + -20)(x + -20) = 385 Calculate the square root of the right side: 19.62141687 Break this problem into two subproblems by setting (x + -20) equal to 19.62141687 and -19.62141687.Subproblem 1
x + -20 = 19.62141687 Simplifying x + -20 = 19.62141687 Reorder the terms: -20 + x = 19.62141687 Solving -20 + x = 19.62141687 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 = 19.62141687 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.62141687 + 20 x = 19.62141687 + 20 Combine like terms: 19.62141687 + 20 = 39.62141687 x = 39.62141687 Simplifying x = 39.62141687Subproblem 2
x + -20 = -19.62141687 Simplifying x + -20 = -19.62141687 Reorder the terms: -20 + x = -19.62141687 Solving -20 + x = -19.62141687 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 = -19.62141687 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.62141687 + 20 x = -19.62141687 + 20 Combine like terms: -19.62141687 + 20 = 0.37858313 x = 0.37858313 Simplifying x = 0.37858313Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.62141687, 0.37858313}
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