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Simplifying 0.15 = 3.9x + 4.9x2 Solving 0.15 = 3.9x + 4.9x2 Solving for variable 'x'. Reorder the terms: 0.15 + -3.9x + -4.9x2 = 3.9x + -3.9x + 4.9x2 + -4.9x2 Combine like terms: 3.9x + -3.9x = 0.0 0.15 + -3.9x + -4.9x2 = 0.0 + 4.9x2 + -4.9x2 0.15 + -3.9x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 0.15 + -3.9x + -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'. -0.0306122449 + 0.7959183673x + x2 = 0 Move the constant term to the right: Add '0.0306122449' to each side of the equation. -0.0306122449 + 0.7959183673x + 0.0306122449 + x2 = 0 + 0.0306122449 Reorder the terms: -0.0306122449 + 0.0306122449 + 0.7959183673x + x2 = 0 + 0.0306122449 Combine like terms: -0.0306122449 + 0.0306122449 = 0.0000000000 0.0000000000 + 0.7959183673x + x2 = 0 + 0.0306122449 0.7959183673x + x2 = 0 + 0.0306122449 Combine like terms: 0 + 0.0306122449 = 0.0306122449 0.7959183673x + x2 = 0.0306122449 The x term is 0.7959183673x. Take half its coefficient (0.3979591837). Square it (0.1583715119) and add it to both sides. Add '0.1583715119' to each side of the equation. 0.7959183673x + 0.1583715119 + x2 = 0.0306122449 + 0.1583715119 Reorder the terms: 0.1583715119 + 0.7959183673x + x2 = 0.0306122449 + 0.1583715119 Combine like terms: 0.0306122449 + 0.1583715119 = 0.1889837568 0.1583715119 + 0.7959183673x + x2 = 0.1889837568 Factor a perfect square on the left side: (x + 0.3979591837)(x + 0.3979591837) = 0.1889837568 Calculate the square root of the right side: 0.434722621 Break this problem into two subproblems by setting (x + 0.3979591837) equal to 0.434722621 and -0.434722621.Subproblem 1
x + 0.3979591837 = 0.434722621 Simplifying x + 0.3979591837 = 0.434722621 Reorder the terms: 0.3979591837 + x = 0.434722621 Solving 0.3979591837 + x = 0.434722621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3979591837' to each side of the equation. 0.3979591837 + -0.3979591837 + x = 0.434722621 + -0.3979591837 Combine like terms: 0.3979591837 + -0.3979591837 = 0.0000000000 0.0000000000 + x = 0.434722621 + -0.3979591837 x = 0.434722621 + -0.3979591837 Combine like terms: 0.434722621 + -0.3979591837 = 0.0367634373 x = 0.0367634373 Simplifying x = 0.0367634373Subproblem 2
x + 0.3979591837 = -0.434722621 Simplifying x + 0.3979591837 = -0.434722621 Reorder the terms: 0.3979591837 + x = -0.434722621 Solving 0.3979591837 + x = -0.434722621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3979591837' to each side of the equation. 0.3979591837 + -0.3979591837 + x = -0.434722621 + -0.3979591837 Combine like terms: 0.3979591837 + -0.3979591837 = 0.0000000000 0.0000000000 + x = -0.434722621 + -0.3979591837 x = -0.434722621 + -0.3979591837 Combine like terms: -0.434722621 + -0.3979591837 = -0.8326818047 x = -0.8326818047 Simplifying x = -0.8326818047Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0367634373, -0.8326818047}
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