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Simplifying 144 = x2 + -3x Reorder the terms: 144 = -3x + x2 Solving 144 = -3x + x2 Solving for variable 'x'. Reorder the terms: 144 + 3x + -1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 144 + 3x + -1x2 = 0 + x2 + -1x2 144 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 144 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + -3x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + -3x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -3x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -3x + x2 = 0 + 144 -3x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -3x + x2 = 144 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 = 144 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 144 + 2.25 Combine like terms: 144 + 2.25 = 146.25 2.25 + -3x + x2 = 146.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (x + -1.5) equal to 12.093386622 and -12.093386622.Subproblem 1
x + -1.5 = 12.093386622 Simplifying x + -1.5 = 12.093386622 Reorder the terms: -1.5 + x = 12.093386622 Solving -1.5 + x = 12.093386622 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 = 12.093386622 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 12.093386622 + 1.5 x = 12.093386622 + 1.5 Combine like terms: 12.093386622 + 1.5 = 13.593386622 x = 13.593386622 Simplifying x = 13.593386622Subproblem 2
x + -1.5 = -12.093386622 Simplifying x + -1.5 = -12.093386622 Reorder the terms: -1.5 + x = -12.093386622 Solving -1.5 + x = -12.093386622 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 = -12.093386622 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -12.093386622 + 1.5 x = -12.093386622 + 1.5 Combine like terms: -12.093386622 + 1.5 = -10.593386622 x = -10.593386622 Simplifying x = -10.593386622Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.593386622, -10.593386622}
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