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Simplifying x2 + -40x + -210 = 0 Reorder the terms: -210 + -40x + x2 = 0 Solving -210 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '210' to each side of the equation. -210 + -40x + 210 + x2 = 0 + 210 Reorder the terms: -210 + 210 + -40x + x2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + -40x + x2 = 0 + 210 -40x + x2 = 0 + 210 Combine like terms: 0 + 210 = 210 -40x + x2 = 210 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 = 210 + 400 Reorder the terms: 400 + -40x + x2 = 210 + 400 Combine like terms: 210 + 400 = 610 400 + -40x + x2 = 610 Factor a perfect square on the left side: (x + -20)(x + -20) = 610 Calculate the square root of the right side: 24.69817807 Break this problem into two subproblems by setting (x + -20) equal to 24.69817807 and -24.69817807.Subproblem 1
x + -20 = 24.69817807 Simplifying x + -20 = 24.69817807 Reorder the terms: -20 + x = 24.69817807 Solving -20 + x = 24.69817807 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 = 24.69817807 + 20 Combine like terms: -20 + 20 = 0 0 + x = 24.69817807 + 20 x = 24.69817807 + 20 Combine like terms: 24.69817807 + 20 = 44.69817807 x = 44.69817807 Simplifying x = 44.69817807Subproblem 2
x + -20 = -24.69817807 Simplifying x + -20 = -24.69817807 Reorder the terms: -20 + x = -24.69817807 Solving -20 + x = -24.69817807 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 = -24.69817807 + 20 Combine like terms: -20 + 20 = 0 0 + x = -24.69817807 + 20 x = -24.69817807 + 20 Combine like terms: -24.69817807 + 20 = -4.69817807 x = -4.69817807 Simplifying x = -4.69817807Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.69817807, -4.69817807}
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