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Simplifying x2 + -4x + -3 = 180 Reorder the terms: -3 + -4x + x2 = 180 Solving -3 + -4x + x2 = 180 Solving for variable 'x'. Reorder the terms: -3 + -180 + -4x + x2 = 180 + -180 Combine like terms: -3 + -180 = -183 -183 + -4x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -183 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '183' to each side of the equation. -183 + -4x + 183 + x2 = 0 + 183 Reorder the terms: -183 + 183 + -4x + x2 = 0 + 183 Combine like terms: -183 + 183 = 0 0 + -4x + x2 = 0 + 183 -4x + x2 = 0 + 183 Combine like terms: 0 + 183 = 183 -4x + x2 = 183 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 = 183 + 4 Reorder the terms: 4 + -4x + x2 = 183 + 4 Combine like terms: 183 + 4 = 187 4 + -4x + x2 = 187 Factor a perfect square on the left side: (x + -2)(x + -2) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (x + -2) equal to 13.674794331 and -13.674794331.Subproblem 1
x + -2 = 13.674794331 Simplifying x + -2 = 13.674794331 Reorder the terms: -2 + x = 13.674794331 Solving -2 + x = 13.674794331 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 = 13.674794331 + 2 Combine like terms: -2 + 2 = 0 0 + x = 13.674794331 + 2 x = 13.674794331 + 2 Combine like terms: 13.674794331 + 2 = 15.674794331 x = 15.674794331 Simplifying x = 15.674794331Subproblem 2
x + -2 = -13.674794331 Simplifying x + -2 = -13.674794331 Reorder the terms: -2 + x = -13.674794331 Solving -2 + x = -13.674794331 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 = -13.674794331 + 2 Combine like terms: -2 + 2 = 0 0 + x = -13.674794331 + 2 x = -13.674794331 + 2 Combine like terms: -13.674794331 + 2 = -11.674794331 x = -11.674794331 Simplifying x = -11.674794331Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.674794331, -11.674794331}
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