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Simplifying 4.5x2 + -135x + -500 = 0 Reorder the terms: -500 + -135x + 4.5x2 = 0 Solving -500 + -135x + 4.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.5 the coefficient of the squared term: Divide each side by '4.5'. -111.1111111 + -30x + x2 = 0 Move the constant term to the right: Add '111.1111111' to each side of the equation. -111.1111111 + -30x + 111.1111111 + x2 = 0 + 111.1111111 Reorder the terms: -111.1111111 + 111.1111111 + -30x + x2 = 0 + 111.1111111 Combine like terms: -111.1111111 + 111.1111111 = 0.0000000 0.0000000 + -30x + x2 = 0 + 111.1111111 -30x + x2 = 0 + 111.1111111 Combine like terms: 0 + 111.1111111 = 111.1111111 -30x + x2 = 111.1111111 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 111.1111111 + 225 Reorder the terms: 225 + -30x + x2 = 111.1111111 + 225 Combine like terms: 111.1111111 + 225 = 336.1111111 225 + -30x + x2 = 336.1111111 Factor a perfect square on the left side: (x + -15)(x + -15) = 336.1111111 Calculate the square root of the right side: 18.333333333 Break this problem into two subproblems by setting (x + -15) equal to 18.333333333 and -18.333333333.Subproblem 1
x + -15 = 18.333333333 Simplifying x + -15 = 18.333333333 Reorder the terms: -15 + x = 18.333333333 Solving -15 + x = 18.333333333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 18.333333333 + 15 Combine like terms: -15 + 15 = 0 0 + x = 18.333333333 + 15 x = 18.333333333 + 15 Combine like terms: 18.333333333 + 15 = 33.333333333 x = 33.333333333 Simplifying x = 33.333333333Subproblem 2
x + -15 = -18.333333333 Simplifying x + -15 = -18.333333333 Reorder the terms: -15 + x = -18.333333333 Solving -15 + x = -18.333333333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -18.333333333 + 15 Combine like terms: -15 + 15 = 0 0 + x = -18.333333333 + 15 x = -18.333333333 + 15 Combine like terms: -18.333333333 + 15 = -3.333333333 x = -3.333333333 Simplifying x = -3.333333333Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.333333333, -3.333333333}
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