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Simplifying 15x2 + -144x + 32 = 0 Reorder the terms: 32 + -144x + 15x2 = 0 Solving 32 + -144x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 2.133333333 + -9.6x + x2 = 0 Move the constant term to the right: Add '-2.133333333' to each side of the equation. 2.133333333 + -9.6x + -2.133333333 + x2 = 0 + -2.133333333 Reorder the terms: 2.133333333 + -2.133333333 + -9.6x + x2 = 0 + -2.133333333 Combine like terms: 2.133333333 + -2.133333333 = 0.000000000 0.000000000 + -9.6x + x2 = 0 + -2.133333333 -9.6x + x2 = 0 + -2.133333333 Combine like terms: 0 + -2.133333333 = -2.133333333 -9.6x + x2 = -2.133333333 The x term is -9.6x. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6x + 23.04 + x2 = -2.133333333 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = -2.133333333 + 23.04 Combine like terms: -2.133333333 + 23.04 = 20.906666667 23.04 + -9.6x + x2 = 20.906666667 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 20.906666667 Calculate the square root of the right side: 4.572380853 Break this problem into two subproblems by setting (x + -4.8) equal to 4.572380853 and -4.572380853.Subproblem 1
x + -4.8 = 4.572380853 Simplifying x + -4.8 = 4.572380853 Reorder the terms: -4.8 + x = 4.572380853 Solving -4.8 + x = 4.572380853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 4.572380853 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 4.572380853 + 4.8 x = 4.572380853 + 4.8 Combine like terms: 4.572380853 + 4.8 = 9.372380853 x = 9.372380853 Simplifying x = 9.372380853Subproblem 2
x + -4.8 = -4.572380853 Simplifying x + -4.8 = -4.572380853 Reorder the terms: -4.8 + x = -4.572380853 Solving -4.8 + x = -4.572380853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = -4.572380853 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -4.572380853 + 4.8 x = -4.572380853 + 4.8 Combine like terms: -4.572380853 + 4.8 = 0.227619147 x = 0.227619147 Simplifying x = 0.227619147Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.372380853, 0.227619147}
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