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Simplifying -1x2 + -40x + -395 = 0 Reorder the terms: -395 + -40x + -1x2 = 0 Solving -395 + -40x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(395 + 40x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(395 + 40x + x2)' equal to zero and attempt to solve: Simplifying 395 + 40x + x2 = 0 Solving 395 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-395' to each side of the equation. 395 + 40x + -395 + x2 = 0 + -395 Reorder the terms: 395 + -395 + 40x + x2 = 0 + -395 Combine like terms: 395 + -395 = 0 0 + 40x + x2 = 0 + -395 40x + x2 = 0 + -395 Combine like terms: 0 + -395 = -395 40x + x2 = -395 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 = -395 + 400 Reorder the terms: 400 + 40x + x2 = -395 + 400 Combine like terms: -395 + 400 = 5 400 + 40x + x2 = 5 Factor a perfect square on the left side: (x + 20)(x + 20) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 20) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 20 = 2.236067978 Simplifying x + 20 = 2.236067978 Reorder the terms: 20 + x = 2.236067978 Solving 20 + x = 2.236067978 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 = 2.236067978 + -20 Combine like terms: 20 + -20 = 0 0 + x = 2.236067978 + -20 x = 2.236067978 + -20 Combine like terms: 2.236067978 + -20 = -17.763932022 x = -17.763932022 Simplifying x = -17.763932022Subproblem 2
x + 20 = -2.236067978 Simplifying x + 20 = -2.236067978 Reorder the terms: 20 + x = -2.236067978 Solving 20 + x = -2.236067978 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 = -2.236067978 + -20 Combine like terms: 20 + -20 = 0 0 + x = -2.236067978 + -20 x = -2.236067978 + -20 Combine like terms: -2.236067978 + -20 = -22.236067978 x = -22.236067978 Simplifying x = -22.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-17.763932022, -22.236067978}Solution
x = {-17.763932022, -22.236067978}
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