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Simplifying x2 + 40x + -700 = 0 Reorder the terms: -700 + 40x + x2 = 0 Solving -700 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '700' to each side of the equation. -700 + 40x + 700 + x2 = 0 + 700 Reorder the terms: -700 + 700 + 40x + x2 = 0 + 700 Combine like terms: -700 + 700 = 0 0 + 40x + x2 = 0 + 700 40x + x2 = 0 + 700 Combine like terms: 0 + 700 = 700 40x + x2 = 700 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 = 700 + 400 Reorder the terms: 400 + 40x + x2 = 700 + 400 Combine like terms: 700 + 400 = 1100 400 + 40x + x2 = 1100 Factor a perfect square on the left side: (x + 20)(x + 20) = 1100 Calculate the square root of the right side: 33.166247904 Break this problem into two subproblems by setting (x + 20) equal to 33.166247904 and -33.166247904.Subproblem 1
x + 20 = 33.166247904 Simplifying x + 20 = 33.166247904 Reorder the terms: 20 + x = 33.166247904 Solving 20 + x = 33.166247904 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 = 33.166247904 + -20 Combine like terms: 20 + -20 = 0 0 + x = 33.166247904 + -20 x = 33.166247904 + -20 Combine like terms: 33.166247904 + -20 = 13.166247904 x = 13.166247904 Simplifying x = 13.166247904Subproblem 2
x + 20 = -33.166247904 Simplifying x + 20 = -33.166247904 Reorder the terms: 20 + x = -33.166247904 Solving 20 + x = -33.166247904 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 = -33.166247904 + -20 Combine like terms: 20 + -20 = 0 0 + x = -33.166247904 + -20 x = -33.166247904 + -20 Combine like terms: -33.166247904 + -20 = -53.166247904 x = -53.166247904 Simplifying x = -53.166247904Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.166247904, -53.166247904}
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