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Simplifying x2 + 2x + -100 = 180 Reorder the terms: -100 + 2x + x2 = 180 Solving -100 + 2x + x2 = 180 Solving for variable 'x'. Reorder the terms: -100 + -180 + 2x + x2 = 180 + -180 Combine like terms: -100 + -180 = -280 -280 + 2x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -280 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '280' to each side of the equation. -280 + 2x + 280 + x2 = 0 + 280 Reorder the terms: -280 + 280 + 2x + x2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + 2x + x2 = 0 + 280 2x + x2 = 0 + 280 Combine like terms: 0 + 280 = 280 2x + x2 = 280 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 280 + 1 Reorder the terms: 1 + 2x + x2 = 280 + 1 Combine like terms: 280 + 1 = 281 1 + 2x + x2 = 281 Factor a perfect square on the left side: (x + 1)(x + 1) = 281 Calculate the square root of the right side: 16.763054614 Break this problem into two subproblems by setting (x + 1) equal to 16.763054614 and -16.763054614.Subproblem 1
x + 1 = 16.763054614 Simplifying x + 1 = 16.763054614 Reorder the terms: 1 + x = 16.763054614 Solving 1 + x = 16.763054614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 16.763054614 + -1 Combine like terms: 1 + -1 = 0 0 + x = 16.763054614 + -1 x = 16.763054614 + -1 Combine like terms: 16.763054614 + -1 = 15.763054614 x = 15.763054614 Simplifying x = 15.763054614Subproblem 2
x + 1 = -16.763054614 Simplifying x + 1 = -16.763054614 Reorder the terms: 1 + x = -16.763054614 Solving 1 + x = -16.763054614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -16.763054614 + -1 Combine like terms: 1 + -1 = 0 0 + x = -16.763054614 + -1 x = -16.763054614 + -1 Combine like terms: -16.763054614 + -1 = -17.763054614 x = -17.763054614 Simplifying x = -17.763054614Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.763054614, -17.763054614}
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