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Simplifying 4.9x2 + -180x + -2 = 0 Reorder the terms: -2 + -180x + 4.9x2 = 0 Solving -2 + -180x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.4081632653 + -36.73469388x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -36.73469388x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -36.73469388x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -36.73469388x + x2 = 0 + 0.4081632653 -36.73469388x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -36.73469388x + x2 = 0.4081632653 The x term is -36.73469388x. Take half its coefficient (-18.36734694). Square it (337.3594336) and add it to both sides. Add '337.3594336' to each side of the equation. -36.73469388x + 337.3594336 + x2 = 0.4081632653 + 337.3594336 Reorder the terms: 337.3594336 + -36.73469388x + x2 = 0.4081632653 + 337.3594336 Combine like terms: 0.4081632653 + 337.3594336 = 337.7675968653 337.3594336 + -36.73469388x + x2 = 337.7675968653 Factor a perfect square on the left side: (x + -18.36734694)(x + -18.36734694) = 337.7675968653 Calculate the square root of the right side: 18.378454692 Break this problem into two subproblems by setting (x + -18.36734694) equal to 18.378454692 and -18.378454692.Subproblem 1
x + -18.36734694 = 18.378454692 Simplifying x + -18.36734694 = 18.378454692 Reorder the terms: -18.36734694 + x = 18.378454692 Solving -18.36734694 + x = 18.378454692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.36734694' to each side of the equation. -18.36734694 + 18.36734694 + x = 18.378454692 + 18.36734694 Combine like terms: -18.36734694 + 18.36734694 = 0.00000000 0.00000000 + x = 18.378454692 + 18.36734694 x = 18.378454692 + 18.36734694 Combine like terms: 18.378454692 + 18.36734694 = 36.745801632 x = 36.745801632 Simplifying x = 36.745801632Subproblem 2
x + -18.36734694 = -18.378454692 Simplifying x + -18.36734694 = -18.378454692 Reorder the terms: -18.36734694 + x = -18.378454692 Solving -18.36734694 + x = -18.378454692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.36734694' to each side of the equation. -18.36734694 + 18.36734694 + x = -18.378454692 + 18.36734694 Combine like terms: -18.36734694 + 18.36734694 = 0.00000000 0.00000000 + x = -18.378454692 + 18.36734694 x = -18.378454692 + 18.36734694 Combine like terms: -18.378454692 + 18.36734694 = -0.011107752 x = -0.011107752 Simplifying x = -0.011107752Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.745801632, -0.011107752}
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