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Simplifying 1.8 = 16x + (0.5)(9.8)(x2) Multiply 0.5 * 9.8 1.8 = 16x + 4.9x2 Solving 1.8 = 16x + 4.9x2 Solving for variable 'x'. Reorder the terms: 1.8 + -16x + -4.9x2 = 16x + -16x + 4.9x2 + -4.9x2 Combine like terms: 16x + -16x = 0 1.8 + -16x + -4.9x2 = 0 + 4.9x2 + -4.9x2 1.8 + -16x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 1.8 + -16x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.3673469388 + 3.265306122x + x2 = 0 Move the constant term to the right: Add '0.3673469388' to each side of the equation. -0.3673469388 + 3.265306122x + 0.3673469388 + x2 = 0 + 0.3673469388 Reorder the terms: -0.3673469388 + 0.3673469388 + 3.265306122x + x2 = 0 + 0.3673469388 Combine like terms: -0.3673469388 + 0.3673469388 = 0.0000000000 0.0000000000 + 3.265306122x + x2 = 0 + 0.3673469388 3.265306122x + x2 = 0 + 0.3673469388 Combine like terms: 0 + 0.3673469388 = 0.3673469388 3.265306122x + x2 = 0.3673469388 The x term is 3.265306122x. Take half its coefficient (1.632653061). Square it (2.665556018) and add it to both sides. Add '2.665556018' to each side of the equation. 3.265306122x + 2.665556018 + x2 = 0.3673469388 + 2.665556018 Reorder the terms: 2.665556018 + 3.265306122x + x2 = 0.3673469388 + 2.665556018 Combine like terms: 0.3673469388 + 2.665556018 = 3.0329029568 2.665556018 + 3.265306122x + x2 = 3.0329029568 Factor a perfect square on the left side: (x + 1.632653061)(x + 1.632653061) = 3.0329029568 Calculate the square root of the right side: 1.741523171 Break this problem into two subproblems by setting (x + 1.632653061) equal to 1.741523171 and -1.741523171.Subproblem 1
x + 1.632653061 = 1.741523171 Simplifying x + 1.632653061 = 1.741523171 Reorder the terms: 1.632653061 + x = 1.741523171 Solving 1.632653061 + x = 1.741523171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.632653061' to each side of the equation. 1.632653061 + -1.632653061 + x = 1.741523171 + -1.632653061 Combine like terms: 1.632653061 + -1.632653061 = 0.000000000 0.000000000 + x = 1.741523171 + -1.632653061 x = 1.741523171 + -1.632653061 Combine like terms: 1.741523171 + -1.632653061 = 0.10887011 x = 0.10887011 Simplifying x = 0.10887011Subproblem 2
x + 1.632653061 = -1.741523171 Simplifying x + 1.632653061 = -1.741523171 Reorder the terms: 1.632653061 + x = -1.741523171 Solving 1.632653061 + x = -1.741523171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.632653061' to each side of the equation. 1.632653061 + -1.632653061 + x = -1.741523171 + -1.632653061 Combine like terms: 1.632653061 + -1.632653061 = 0.000000000 0.000000000 + x = -1.741523171 + -1.632653061 x = -1.741523171 + -1.632653061 Combine like terms: -1.741523171 + -1.632653061 = -3.374176232 x = -3.374176232 Simplifying x = -3.374176232Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.10887011, -3.374176232}
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