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Simplifying 12 + 10x + 0.5x2 = 900 Solving 12 + 10x + 0.5x2 = 900 Solving for variable 'x'. Reorder the terms: 12 + -900 + 10x + 0.5x2 = 900 + -900 Combine like terms: 12 + -900 = -888 -888 + 10x + 0.5x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -888 + 10x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -1776 + 20x + x2 = 0 Move the constant term to the right: Add '1776' to each side of the equation. -1776 + 20x + 1776 + x2 = 0 + 1776 Reorder the terms: -1776 + 1776 + 20x + x2 = 0 + 1776 Combine like terms: -1776 + 1776 = 0 0 + 20x + x2 = 0 + 1776 20x + x2 = 0 + 1776 Combine like terms: 0 + 1776 = 1776 20x + x2 = 1776 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 1776 + 100 Reorder the terms: 100 + 20x + x2 = 1776 + 100 Combine like terms: 1776 + 100 = 1876 100 + 20x + x2 = 1876 Factor a perfect square on the left side: (x + 10)(x + 10) = 1876 Calculate the square root of the right side: 43.312815655 Break this problem into two subproblems by setting (x + 10) equal to 43.312815655 and -43.312815655.Subproblem 1
x + 10 = 43.312815655 Simplifying x + 10 = 43.312815655 Reorder the terms: 10 + x = 43.312815655 Solving 10 + x = 43.312815655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 43.312815655 + -10 Combine like terms: 10 + -10 = 0 0 + x = 43.312815655 + -10 x = 43.312815655 + -10 Combine like terms: 43.312815655 + -10 = 33.312815655 x = 33.312815655 Simplifying x = 33.312815655Subproblem 2
x + 10 = -43.312815655 Simplifying x + 10 = -43.312815655 Reorder the terms: 10 + x = -43.312815655 Solving 10 + x = -43.312815655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -43.312815655 + -10 Combine like terms: 10 + -10 = 0 0 + x = -43.312815655 + -10 x = -43.312815655 + -10 Combine like terms: -43.312815655 + -10 = -53.312815655 x = -53.312815655 Simplifying x = -53.312815655Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.312815655, -53.312815655}
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