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Simplifying x2 + 4.5x + -1620 = 0 Reorder the terms: -1620 + 4.5x + x2 = 0 Solving -1620 + 4.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1620' to each side of the equation. -1620 + 4.5x + 1620 + x2 = 0 + 1620 Reorder the terms: -1620 + 1620 + 4.5x + x2 = 0 + 1620 Combine like terms: -1620 + 1620 = 0 0 + 4.5x + x2 = 0 + 1620 4.5x + x2 = 0 + 1620 Combine like terms: 0 + 1620 = 1620 4.5x + x2 = 1620 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 1620 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 1620 + 5.0625 Combine like terms: 1620 + 5.0625 = 1625.0625 5.0625 + 4.5x + x2 = 1625.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 1625.0625 Calculate the square root of the right side: 40.312063951 Break this problem into two subproblems by setting (x + 2.25) equal to 40.312063951 and -40.312063951.Subproblem 1
x + 2.25 = 40.312063951 Simplifying x + 2.25 = 40.312063951 Reorder the terms: 2.25 + x = 40.312063951 Solving 2.25 + x = 40.312063951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 40.312063951 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 40.312063951 + -2.25 x = 40.312063951 + -2.25 Combine like terms: 40.312063951 + -2.25 = 38.062063951 x = 38.062063951 Simplifying x = 38.062063951Subproblem 2
x + 2.25 = -40.312063951 Simplifying x + 2.25 = -40.312063951 Reorder the terms: 2.25 + x = -40.312063951 Solving 2.25 + x = -40.312063951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -40.312063951 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -40.312063951 + -2.25 x = -40.312063951 + -2.25 Combine like terms: -40.312063951 + -2.25 = -42.562063951 x = -42.562063951 Simplifying x = -42.562063951Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.062063951, -42.562063951}
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