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Simplifying 45x2 + 146x + -242 = 0 Reorder the terms: -242 + 146x + 45x2 = 0 Solving -242 + 146x + 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'. -5.377777778 + 3.244444444x + x2 = 0 Move the constant term to the right: Add '5.377777778' to each side of the equation. -5.377777778 + 3.244444444x + 5.377777778 + x2 = 0 + 5.377777778 Reorder the terms: -5.377777778 + 5.377777778 + 3.244444444x + x2 = 0 + 5.377777778 Combine like terms: -5.377777778 + 5.377777778 = 0.000000000 0.000000000 + 3.244444444x + x2 = 0 + 5.377777778 3.244444444x + x2 = 0 + 5.377777778 Combine like terms: 0 + 5.377777778 = 5.377777778 3.244444444x + x2 = 5.377777778 The x term is 3.244444444x. Take half its coefficient (1.622222222). Square it (2.631604938) and add it to both sides. Add '2.631604938' to each side of the equation. 3.244444444x + 2.631604938 + x2 = 5.377777778 + 2.631604938 Reorder the terms: 2.631604938 + 3.244444444x + x2 = 5.377777778 + 2.631604938 Combine like terms: 5.377777778 + 2.631604938 = 8.009382716 2.631604938 + 3.244444444x + x2 = 8.009382716 Factor a perfect square on the left side: (x + 1.622222222)(x + 1.622222222) = 8.009382716 Calculate the square root of the right side: 2.830085284 Break this problem into two subproblems by setting (x + 1.622222222) equal to 2.830085284 and -2.830085284.Subproblem 1
x + 1.622222222 = 2.830085284 Simplifying x + 1.622222222 = 2.830085284 Reorder the terms: 1.622222222 + x = 2.830085284 Solving 1.622222222 + x = 2.830085284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.622222222' to each side of the equation. 1.622222222 + -1.622222222 + x = 2.830085284 + -1.622222222 Combine like terms: 1.622222222 + -1.622222222 = 0.000000000 0.000000000 + x = 2.830085284 + -1.622222222 x = 2.830085284 + -1.622222222 Combine like terms: 2.830085284 + -1.622222222 = 1.207863062 x = 1.207863062 Simplifying x = 1.207863062Subproblem 2
x + 1.622222222 = -2.830085284 Simplifying x + 1.622222222 = -2.830085284 Reorder the terms: 1.622222222 + x = -2.830085284 Solving 1.622222222 + x = -2.830085284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.622222222' to each side of the equation. 1.622222222 + -1.622222222 + x = -2.830085284 + -1.622222222 Combine like terms: 1.622222222 + -1.622222222 = 0.000000000 0.000000000 + x = -2.830085284 + -1.622222222 x = -2.830085284 + -1.622222222 Combine like terms: -2.830085284 + -1.622222222 = -4.452307506 x = -4.452307506 Simplifying x = -4.452307506Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.207863062, -4.452307506}
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