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Simplifying x2 + 4x + -23 = 180 Reorder the terms: -23 + 4x + x2 = 180 Solving -23 + 4x + x2 = 180 Solving for variable 'x'. Reorder the terms: -23 + -180 + 4x + x2 = 180 + -180 Combine like terms: -23 + -180 = -203 -203 + 4x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -203 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '203' to each side of the equation. -203 + 4x + 203 + x2 = 0 + 203 Reorder the terms: -203 + 203 + 4x + x2 = 0 + 203 Combine like terms: -203 + 203 = 0 0 + 4x + x2 = 0 + 203 4x + x2 = 0 + 203 Combine like terms: 0 + 203 = 203 4x + x2 = 203 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 203 + 4 Reorder the terms: 4 + 4x + x2 = 203 + 4 Combine like terms: 203 + 4 = 207 4 + 4x + x2 = 207 Factor a perfect square on the left side: (x + 2)(x + 2) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (x + 2) equal to 14.38749457 and -14.38749457.Subproblem 1
x + 2 = 14.38749457 Simplifying x + 2 = 14.38749457 Reorder the terms: 2 + x = 14.38749457 Solving 2 + x = 14.38749457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 14.38749457 + -2 Combine like terms: 2 + -2 = 0 0 + x = 14.38749457 + -2 x = 14.38749457 + -2 Combine like terms: 14.38749457 + -2 = 12.38749457 x = 12.38749457 Simplifying x = 12.38749457Subproblem 2
x + 2 = -14.38749457 Simplifying x + 2 = -14.38749457 Reorder the terms: 2 + x = -14.38749457 Solving 2 + x = -14.38749457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -14.38749457 + -2 Combine like terms: 2 + -2 = 0 0 + x = -14.38749457 + -2 x = -14.38749457 + -2 Combine like terms: -14.38749457 + -2 = -16.38749457 x = -16.38749457 Simplifying x = -16.38749457Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.38749457, -16.38749457}
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