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Simplifying x2 + 40x + -1000 = 10 Reorder the terms: -1000 + 40x + x2 = 10 Solving -1000 + 40x + x2 = 10 Solving for variable 'x'. Reorder the terms: -1000 + -10 + 40x + x2 = 10 + -10 Combine like terms: -1000 + -10 = -1010 -1010 + 40x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -1010 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1010' to each side of the equation. -1010 + 40x + 1010 + x2 = 0 + 1010 Reorder the terms: -1010 + 1010 + 40x + x2 = 0 + 1010 Combine like terms: -1010 + 1010 = 0 0 + 40x + x2 = 0 + 1010 40x + x2 = 0 + 1010 Combine like terms: 0 + 1010 = 1010 40x + x2 = 1010 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 = 1010 + 400 Reorder the terms: 400 + 40x + x2 = 1010 + 400 Combine like terms: 1010 + 400 = 1410 400 + 40x + x2 = 1410 Factor a perfect square on the left side: (x + 20)(x + 20) = 1410 Calculate the square root of the right side: 37.549966711 Break this problem into two subproblems by setting (x + 20) equal to 37.549966711 and -37.549966711.Subproblem 1
x + 20 = 37.549966711 Simplifying x + 20 = 37.549966711 Reorder the terms: 20 + x = 37.549966711 Solving 20 + x = 37.549966711 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 = 37.549966711 + -20 Combine like terms: 20 + -20 = 0 0 + x = 37.549966711 + -20 x = 37.549966711 + -20 Combine like terms: 37.549966711 + -20 = 17.549966711 x = 17.549966711 Simplifying x = 17.549966711Subproblem 2
x + 20 = -37.549966711 Simplifying x + 20 = -37.549966711 Reorder the terms: 20 + x = -37.549966711 Solving 20 + x = -37.549966711 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 = -37.549966711 + -20 Combine like terms: 20 + -20 = 0 0 + x = -37.549966711 + -20 x = -37.549966711 + -20 Combine like terms: -37.549966711 + -20 = -57.549966711 x = -57.549966711 Simplifying x = -57.549966711Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.549966711, -57.549966711}
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