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Simplifying 1.5x2 + -36x + 45 = 0 Reorder the terms: 45 + -36x + 1.5x2 = 0 Solving 45 + -36x + 1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 30 + -24x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -24x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -24x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -24x + x2 = 0 + -30 -24x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -24x + x2 = -30 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -30 + 144 Reorder the terms: 144 + -24x + x2 = -30 + 144 Combine like terms: -30 + 144 = 114 144 + -24x + x2 = 114 Factor a perfect square on the left side: (x + -12)(x + -12) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + -12) equal to 10.677078252 and -10.677078252.Subproblem 1
x + -12 = 10.677078252 Simplifying x + -12 = 10.677078252 Reorder the terms: -12 + x = 10.677078252 Solving -12 + x = 10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 10.677078252 + 12 Combine like terms: -12 + 12 = 0 0 + x = 10.677078252 + 12 x = 10.677078252 + 12 Combine like terms: 10.677078252 + 12 = 22.677078252 x = 22.677078252 Simplifying x = 22.677078252Subproblem 2
x + -12 = -10.677078252 Simplifying x + -12 = -10.677078252 Reorder the terms: -12 + x = -10.677078252 Solving -12 + x = -10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -10.677078252 + 12 Combine like terms: -12 + 12 = 0 0 + x = -10.677078252 + 12 x = -10.677078252 + 12 Combine like terms: -10.677078252 + 12 = 1.322921748 x = 1.322921748 Simplifying x = 1.322921748Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.677078252, 1.322921748}
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