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Simplifying x2 + -40x + -3425 = 0 Reorder the terms: -3425 + -40x + x2 = 0 Solving -3425 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3425' to each side of the equation. -3425 + -40x + 3425 + x2 = 0 + 3425 Reorder the terms: -3425 + 3425 + -40x + x2 = 0 + 3425 Combine like terms: -3425 + 3425 = 0 0 + -40x + x2 = 0 + 3425 -40x + x2 = 0 + 3425 Combine like terms: 0 + 3425 = 3425 -40x + x2 = 3425 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 = 3425 + 400 Reorder the terms: 400 + -40x + x2 = 3425 + 400 Combine like terms: 3425 + 400 = 3825 400 + -40x + x2 = 3825 Factor a perfect square on the left side: (x + -20)(x + -20) = 3825 Calculate the square root of the right side: 61.846584384 Break this problem into two subproblems by setting (x + -20) equal to 61.846584384 and -61.846584384.Subproblem 1
x + -20 = 61.846584384 Simplifying x + -20 = 61.846584384 Reorder the terms: -20 + x = 61.846584384 Solving -20 + x = 61.846584384 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 = 61.846584384 + 20 Combine like terms: -20 + 20 = 0 0 + x = 61.846584384 + 20 x = 61.846584384 + 20 Combine like terms: 61.846584384 + 20 = 81.846584384 x = 81.846584384 Simplifying x = 81.846584384Subproblem 2
x + -20 = -61.846584384 Simplifying x + -20 = -61.846584384 Reorder the terms: -20 + x = -61.846584384 Solving -20 + x = -61.846584384 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 = -61.846584384 + 20 Combine like terms: -20 + 20 = 0 0 + x = -61.846584384 + 20 x = -61.846584384 + 20 Combine like terms: -61.846584384 + 20 = -41.846584384 x = -41.846584384 Simplifying x = -41.846584384Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.846584384, -41.846584384}
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