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Simplifying 4x2 + -179x + -180 = 0 Reorder the terms: -180 + -179x + 4x2 = 0 Solving -180 + -179x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -45 + -44.75x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -44.75x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -44.75x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -44.75x + x2 = 0 + 45 -44.75x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -44.75x + x2 = 45 The x term is -44.75x. Take half its coefficient (-22.375). Square it (500.640625) and add it to both sides. Add '500.640625' to each side of the equation. -44.75x + 500.640625 + x2 = 45 + 500.640625 Reorder the terms: 500.640625 + -44.75x + x2 = 45 + 500.640625 Combine like terms: 45 + 500.640625 = 545.640625 500.640625 + -44.75x + x2 = 545.640625 Factor a perfect square on the left side: (x + -22.375)(x + -22.375) = 545.640625 Calculate the square root of the right side: 23.35895171 Break this problem into two subproblems by setting (x + -22.375) equal to 23.35895171 and -23.35895171.Subproblem 1
x + -22.375 = 23.35895171 Simplifying x + -22.375 = 23.35895171 Reorder the terms: -22.375 + x = 23.35895171 Solving -22.375 + x = 23.35895171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.375' to each side of the equation. -22.375 + 22.375 + x = 23.35895171 + 22.375 Combine like terms: -22.375 + 22.375 = 0.000 0.000 + x = 23.35895171 + 22.375 x = 23.35895171 + 22.375 Combine like terms: 23.35895171 + 22.375 = 45.73395171 x = 45.73395171 Simplifying x = 45.73395171Subproblem 2
x + -22.375 = -23.35895171 Simplifying x + -22.375 = -23.35895171 Reorder the terms: -22.375 + x = -23.35895171 Solving -22.375 + x = -23.35895171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.375' to each side of the equation. -22.375 + 22.375 + x = -23.35895171 + 22.375 Combine like terms: -22.375 + 22.375 = 0.000 0.000 + x = -23.35895171 + 22.375 x = -23.35895171 + 22.375 Combine like terms: -23.35895171 + 22.375 = -0.98395171 x = -0.98395171 Simplifying x = -0.98395171Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.73395171, -0.98395171}
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