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Simplifying x2 + 40x + -4200 = 0 Reorder the terms: -4200 + 40x + x2 = 0 Solving -4200 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4200' to each side of the equation. -4200 + 40x + 4200 + x2 = 0 + 4200 Reorder the terms: -4200 + 4200 + 40x + x2 = 0 + 4200 Combine like terms: -4200 + 4200 = 0 0 + 40x + x2 = 0 + 4200 40x + x2 = 0 + 4200 Combine like terms: 0 + 4200 = 4200 40x + x2 = 4200 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 = 4200 + 400 Reorder the terms: 400 + 40x + x2 = 4200 + 400 Combine like terms: 4200 + 400 = 4600 400 + 40x + x2 = 4600 Factor a perfect square on the left side: (x + 20)(x + 20) = 4600 Calculate the square root of the right side: 67.823299831 Break this problem into two subproblems by setting (x + 20) equal to 67.823299831 and -67.823299831.Subproblem 1
x + 20 = 67.823299831 Simplifying x + 20 = 67.823299831 Reorder the terms: 20 + x = 67.823299831 Solving 20 + x = 67.823299831 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 = 67.823299831 + -20 Combine like terms: 20 + -20 = 0 0 + x = 67.823299831 + -20 x = 67.823299831 + -20 Combine like terms: 67.823299831 + -20 = 47.823299831 x = 47.823299831 Simplifying x = 47.823299831Subproblem 2
x + 20 = -67.823299831 Simplifying x + 20 = -67.823299831 Reorder the terms: 20 + x = -67.823299831 Solving 20 + x = -67.823299831 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 = -67.823299831 + -20 Combine like terms: 20 + -20 = 0 0 + x = -67.823299831 + -20 x = -67.823299831 + -20 Combine like terms: -67.823299831 + -20 = -87.823299831 x = -87.823299831 Simplifying x = -87.823299831Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.823299831, -87.823299831}
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