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Simplifying -1.5x2 + 33x + -75x = 16 Reorder the terms: 33x + -75x + -1.5x2 = 16 Combine like terms: 33x + -75x = -42x -42x + -1.5x2 = 16 Solving -42x + -1.5x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -42x + -1.5x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -42x + -1.5x2 = 0 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. 10.66666667 + 28x + x2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + 28x + -10.66666667 + x2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + 28x + x2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + 28x + x2 = 0 + -10.66666667 28x + x2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 28x + x2 = -10.66666667 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -10.66666667 + 196 Reorder the terms: 196 + 28x + x2 = -10.66666667 + 196 Combine like terms: -10.66666667 + 196 = 185.33333333 196 + 28x + x2 = 185.33333333 Factor a perfect square on the left side: (x + 14)(x + 14) = 185.33333333 Calculate the square root of the right side: 13.613718571 Break this problem into two subproblems by setting (x + 14) equal to 13.613718571 and -13.613718571.Subproblem 1
x + 14 = 13.613718571 Simplifying x + 14 = 13.613718571 Reorder the terms: 14 + x = 13.613718571 Solving 14 + x = 13.613718571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 13.613718571 + -14 Combine like terms: 14 + -14 = 0 0 + x = 13.613718571 + -14 x = 13.613718571 + -14 Combine like terms: 13.613718571 + -14 = -0.386281429 x = -0.386281429 Simplifying x = -0.386281429Subproblem 2
x + 14 = -13.613718571 Simplifying x + 14 = -13.613718571 Reorder the terms: 14 + x = -13.613718571 Solving 14 + x = -13.613718571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -13.613718571 + -14 Combine like terms: 14 + -14 = 0 0 + x = -13.613718571 + -14 x = -13.613718571 + -14 Combine like terms: -13.613718571 + -14 = -27.613718571 x = -27.613718571 Simplifying x = -27.613718571Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.386281429, -27.613718571}
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