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Simplifying 0.15x2 + 2.7x = 153 Reorder the terms: 2.7x + 0.15x2 = 153 Solving 2.7x + 0.15x2 = 153 Solving for variable 'x'. Reorder the terms: -153 + 2.7x + 0.15x2 = 153 + -153 Combine like terms: 153 + -153 = 0 -153 + 2.7x + 0.15x2 = 0 Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. -1020 + 18x + x2 = 0 Move the constant term to the right: Add '1020' to each side of the equation. -1020 + 18x + 1020 + x2 = 0 + 1020 Reorder the terms: -1020 + 1020 + 18x + x2 = 0 + 1020 Combine like terms: -1020 + 1020 = 0 0 + 18x + x2 = 0 + 1020 18x + x2 = 0 + 1020 Combine like terms: 0 + 1020 = 1020 18x + x2 = 1020 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 1020 + 81 Reorder the terms: 81 + 18x + x2 = 1020 + 81 Combine like terms: 1020 + 81 = 1101 81 + 18x + x2 = 1101 Factor a perfect square on the left side: (x + 9)(x + 9) = 1101 Calculate the square root of the right side: 33.181320046 Break this problem into two subproblems by setting (x + 9) equal to 33.181320046 and -33.181320046.Subproblem 1
x + 9 = 33.181320046 Simplifying x + 9 = 33.181320046 Reorder the terms: 9 + x = 33.181320046 Solving 9 + x = 33.181320046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 33.181320046 + -9 Combine like terms: 9 + -9 = 0 0 + x = 33.181320046 + -9 x = 33.181320046 + -9 Combine like terms: 33.181320046 + -9 = 24.181320046 x = 24.181320046 Simplifying x = 24.181320046Subproblem 2
x + 9 = -33.181320046 Simplifying x + 9 = -33.181320046 Reorder the terms: 9 + x = -33.181320046 Solving 9 + x = -33.181320046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -33.181320046 + -9 Combine like terms: 9 + -9 = 0 0 + x = -33.181320046 + -9 x = -33.181320046 + -9 Combine like terms: -33.181320046 + -9 = -42.181320046 x = -42.181320046 Simplifying x = -42.181320046Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.181320046, -42.181320046}
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