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Simplifying 0 = x2 + -3x + -146 Reorder the terms: 0 = -146 + -3x + x2 Solving 0 = -146 + -3x + x2 Solving for variable 'x'. Combine like terms: 0 + 146 = 146 146 + 3x + -1x2 = -146 + -3x + x2 + 146 + 3x + -1x2 Reorder the terms: 146 + 3x + -1x2 = -146 + 146 + -3x + 3x + x2 + -1x2 Combine like terms: -146 + 146 = 0 146 + 3x + -1x2 = 0 + -3x + 3x + x2 + -1x2 146 + 3x + -1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 146 + 3x + -1x2 = 0 + x2 + -1x2 146 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 146 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -146 + -3x + x2 = 0 Move the constant term to the right: Add '146' to each side of the equation. -146 + -3x + 146 + x2 = 0 + 146 Reorder the terms: -146 + 146 + -3x + x2 = 0 + 146 Combine like terms: -146 + 146 = 0 0 + -3x + x2 = 0 + 146 -3x + x2 = 0 + 146 Combine like terms: 0 + 146 = 146 -3x + x2 = 146 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 146 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 146 + 2.25 Combine like terms: 146 + 2.25 = 148.25 2.25 + -3x + x2 = 148.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 148.25 Calculate the square root of the right side: 12.175795662 Break this problem into two subproblems by setting (x + -1.5) equal to 12.175795662 and -12.175795662.Subproblem 1
x + -1.5 = 12.175795662 Simplifying x + -1.5 = 12.175795662 Reorder the terms: -1.5 + x = 12.175795662 Solving -1.5 + x = 12.175795662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 12.175795662 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 12.175795662 + 1.5 x = 12.175795662 + 1.5 Combine like terms: 12.175795662 + 1.5 = 13.675795662 x = 13.675795662 Simplifying x = 13.675795662Subproblem 2
x + -1.5 = -12.175795662 Simplifying x + -1.5 = -12.175795662 Reorder the terms: -1.5 + x = -12.175795662 Solving -1.5 + x = -12.175795662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -12.175795662 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -12.175795662 + 1.5 x = -12.175795662 + 1.5 Combine like terms: -12.175795662 + 1.5 = -10.675795662 x = -10.675795662 Simplifying x = -10.675795662Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.675795662, -10.675795662}
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