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Simplifying 45x2 + -468x + -2360 = 0 Reorder the terms: -2360 + -468x + 45x2 = 0 Solving -2360 + -468x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -52.44444444 + -10.4x + x2 = 0 Move the constant term to the right: Add '52.44444444' to each side of the equation. -52.44444444 + -10.4x + 52.44444444 + x2 = 0 + 52.44444444 Reorder the terms: -52.44444444 + 52.44444444 + -10.4x + x2 = 0 + 52.44444444 Combine like terms: -52.44444444 + 52.44444444 = 0.00000000 0.00000000 + -10.4x + x2 = 0 + 52.44444444 -10.4x + x2 = 0 + 52.44444444 Combine like terms: 0 + 52.44444444 = 52.44444444 -10.4x + x2 = 52.44444444 The x term is -10.4x. Take half its coefficient (-5.2). Square it (27.04) and add it to both sides. Add '27.04' to each side of the equation. -10.4x + 27.04 + x2 = 52.44444444 + 27.04 Reorder the terms: 27.04 + -10.4x + x2 = 52.44444444 + 27.04 Combine like terms: 52.44444444 + 27.04 = 79.48444444 27.04 + -10.4x + x2 = 79.48444444 Factor a perfect square on the left side: (x + -5.2)(x + -5.2) = 79.48444444 Calculate the square root of the right side: 8.915404895 Break this problem into two subproblems by setting (x + -5.2) equal to 8.915404895 and -8.915404895.Subproblem 1
x + -5.2 = 8.915404895 Simplifying x + -5.2 = 8.915404895 Reorder the terms: -5.2 + x = 8.915404895 Solving -5.2 + x = 8.915404895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.2' to each side of the equation. -5.2 + 5.2 + x = 8.915404895 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x = 8.915404895 + 5.2 x = 8.915404895 + 5.2 Combine like terms: 8.915404895 + 5.2 = 14.115404895 x = 14.115404895 Simplifying x = 14.115404895Subproblem 2
x + -5.2 = -8.915404895 Simplifying x + -5.2 = -8.915404895 Reorder the terms: -5.2 + x = -8.915404895 Solving -5.2 + x = -8.915404895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.2' to each side of the equation. -5.2 + 5.2 + x = -8.915404895 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x = -8.915404895 + 5.2 x = -8.915404895 + 5.2 Combine like terms: -8.915404895 + 5.2 = -3.715404895 x = -3.715404895 Simplifying x = -3.715404895Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.115404895, -3.715404895}
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