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Simplifying 5x2 + -162x + -1008 = 0 Reorder the terms: -1008 + -162x + 5x2 = 0 Solving -1008 + -162x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -201.6 + -32.4x + x2 = 0 Move the constant term to the right: Add '201.6' to each side of the equation. -201.6 + -32.4x + 201.6 + x2 = 0 + 201.6 Reorder the terms: -201.6 + 201.6 + -32.4x + x2 = 0 + 201.6 Combine like terms: -201.6 + 201.6 = 0.0 0.0 + -32.4x + x2 = 0 + 201.6 -32.4x + x2 = 0 + 201.6 Combine like terms: 0 + 201.6 = 201.6 -32.4x + x2 = 201.6 The x term is -32.4x. Take half its coefficient (-16.2). Square it (262.44) and add it to both sides. Add '262.44' to each side of the equation. -32.4x + 262.44 + x2 = 201.6 + 262.44 Reorder the terms: 262.44 + -32.4x + x2 = 201.6 + 262.44 Combine like terms: 201.6 + 262.44 = 464.04 262.44 + -32.4x + x2 = 464.04 Factor a perfect square on the left side: (x + -16.2)(x + -16.2) = 464.04 Calculate the square root of the right side: 21.541587685 Break this problem into two subproblems by setting (x + -16.2) equal to 21.541587685 and -21.541587685.Subproblem 1
x + -16.2 = 21.541587685 Simplifying x + -16.2 = 21.541587685 Reorder the terms: -16.2 + x = 21.541587685 Solving -16.2 + x = 21.541587685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.2' to each side of the equation. -16.2 + 16.2 + x = 21.541587685 + 16.2 Combine like terms: -16.2 + 16.2 = 0.0 0.0 + x = 21.541587685 + 16.2 x = 21.541587685 + 16.2 Combine like terms: 21.541587685 + 16.2 = 37.741587685 x = 37.741587685 Simplifying x = 37.741587685Subproblem 2
x + -16.2 = -21.541587685 Simplifying x + -16.2 = -21.541587685 Reorder the terms: -16.2 + x = -21.541587685 Solving -16.2 + x = -21.541587685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.2' to each side of the equation. -16.2 + 16.2 + x = -21.541587685 + 16.2 Combine like terms: -16.2 + 16.2 = 0.0 0.0 + x = -21.541587685 + 16.2 x = -21.541587685 + 16.2 Combine like terms: -21.541587685 + 16.2 = -5.341587685 x = -5.341587685 Simplifying x = -5.341587685Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.741587685, -5.341587685}
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