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Simplifying x2 + 40x + -10000 = 0 Reorder the terms: -10000 + 40x + x2 = 0 Solving -10000 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 40x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 40x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 40x + x2 = 0 + 10000 40x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 40x + x2 = 10000 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 = 10000 + 400 Reorder the terms: 400 + 40x + x2 = 10000 + 400 Combine like terms: 10000 + 400 = 10400 400 + 40x + x2 = 10400 Factor a perfect square on the left side: (x + 20)(x + 20) = 10400 Calculate the square root of the right side: 101.980390272 Break this problem into two subproblems by setting (x + 20) equal to 101.980390272 and -101.980390272.Subproblem 1
x + 20 = 101.980390272 Simplifying x + 20 = 101.980390272 Reorder the terms: 20 + x = 101.980390272 Solving 20 + x = 101.980390272 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 = 101.980390272 + -20 Combine like terms: 20 + -20 = 0 0 + x = 101.980390272 + -20 x = 101.980390272 + -20 Combine like terms: 101.980390272 + -20 = 81.980390272 x = 81.980390272 Simplifying x = 81.980390272Subproblem 2
x + 20 = -101.980390272 Simplifying x + 20 = -101.980390272 Reorder the terms: 20 + x = -101.980390272 Solving 20 + x = -101.980390272 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 = -101.980390272 + -20 Combine like terms: 20 + -20 = 0 0 + x = -101.980390272 + -20 x = -101.980390272 + -20 Combine like terms: -101.980390272 + -20 = -121.980390272 x = -121.980390272 Simplifying x = -121.980390272Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.980390272, -121.980390272}
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