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Simplifying 5x2 + 144x + -60 = 456 Reorder the terms: -60 + 144x + 5x2 = 456 Solving -60 + 144x + 5x2 = 456 Solving for variable 'x'. Reorder the terms: -60 + -456 + 144x + 5x2 = 456 + -456 Combine like terms: -60 + -456 = -516 -516 + 144x + 5x2 = 456 + -456 Combine like terms: 456 + -456 = 0 -516 + 144x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -103.2 + 28.8x + x2 = 0 Move the constant term to the right: Add '103.2' to each side of the equation. -103.2 + 28.8x + 103.2 + x2 = 0 + 103.2 Reorder the terms: -103.2 + 103.2 + 28.8x + x2 = 0 + 103.2 Combine like terms: -103.2 + 103.2 = 0.0 0.0 + 28.8x + x2 = 0 + 103.2 28.8x + x2 = 0 + 103.2 Combine like terms: 0 + 103.2 = 103.2 28.8x + x2 = 103.2 The x term is 28.8x. Take half its coefficient (14.4). Square it (207.36) and add it to both sides. Add '207.36' to each side of the equation. 28.8x + 207.36 + x2 = 103.2 + 207.36 Reorder the terms: 207.36 + 28.8x + x2 = 103.2 + 207.36 Combine like terms: 103.2 + 207.36 = 310.56 207.36 + 28.8x + x2 = 310.56 Factor a perfect square on the left side: (x + 14.4)(x + 14.4) = 310.56 Calculate the square root of the right side: 17.622712618 Break this problem into two subproblems by setting (x + 14.4) equal to 17.622712618 and -17.622712618.Subproblem 1
x + 14.4 = 17.622712618 Simplifying x + 14.4 = 17.622712618 Reorder the terms: 14.4 + x = 17.622712618 Solving 14.4 + x = 17.622712618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.4' to each side of the equation. 14.4 + -14.4 + x = 17.622712618 + -14.4 Combine like terms: 14.4 + -14.4 = 0.0 0.0 + x = 17.622712618 + -14.4 x = 17.622712618 + -14.4 Combine like terms: 17.622712618 + -14.4 = 3.222712618 x = 3.222712618 Simplifying x = 3.222712618Subproblem 2
x + 14.4 = -17.622712618 Simplifying x + 14.4 = -17.622712618 Reorder the terms: 14.4 + x = -17.622712618 Solving 14.4 + x = -17.622712618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.4' to each side of the equation. 14.4 + -14.4 + x = -17.622712618 + -14.4 Combine like terms: 14.4 + -14.4 = 0.0 0.0 + x = -17.622712618 + -14.4 x = -17.622712618 + -14.4 Combine like terms: -17.622712618 + -14.4 = -32.022712618 x = -32.022712618 Simplifying x = -32.022712618Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.222712618, -32.022712618}
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