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Simplifying -4.9x2 + 6.2x + 1.9 = 0 Reorder the terms: 1.9 + 6.2x + -4.9x2 = 0 Solving 1.9 + 6.2x + -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'. -0.387755102 + -1.265306122x + x2 = 0 Move the constant term to the right: Add '0.387755102' to each side of the equation. -0.387755102 + -1.265306122x + 0.387755102 + x2 = 0 + 0.387755102 Reorder the terms: -0.387755102 + 0.387755102 + -1.265306122x + x2 = 0 + 0.387755102 Combine like terms: -0.387755102 + 0.387755102 = 0.000000000 0.000000000 + -1.265306122x + x2 = 0 + 0.387755102 -1.265306122x + x2 = 0 + 0.387755102 Combine like terms: 0 + 0.387755102 = 0.387755102 -1.265306122x + x2 = 0.387755102 The x term is -1.265306122x. Take half its coefficient (-0.632653061). Square it (0.4002498956) and add it to both sides. Add '0.4002498956' to each side of the equation. -1.265306122x + 0.4002498956 + x2 = 0.387755102 + 0.4002498956 Reorder the terms: 0.4002498956 + -1.265306122x + x2 = 0.387755102 + 0.4002498956 Combine like terms: 0.387755102 + 0.4002498956 = 0.7880049976 0.4002498956 + -1.265306122x + x2 = 0.7880049976 Factor a perfect square on the left side: (x + -0.632653061)(x + -0.632653061) = 0.7880049976 Calculate the square root of the right side: 0.887696456 Break this problem into two subproblems by setting (x + -0.632653061) equal to 0.887696456 and -0.887696456.Subproblem 1
x + -0.632653061 = 0.887696456 Simplifying x + -0.632653061 = 0.887696456 Reorder the terms: -0.632653061 + x = 0.887696456 Solving -0.632653061 + x = 0.887696456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.632653061' to each side of the equation. -0.632653061 + 0.632653061 + x = 0.887696456 + 0.632653061 Combine like terms: -0.632653061 + 0.632653061 = 0.000000000 0.000000000 + x = 0.887696456 + 0.632653061 x = 0.887696456 + 0.632653061 Combine like terms: 0.887696456 + 0.632653061 = 1.520349517 x = 1.520349517 Simplifying x = 1.520349517Subproblem 2
x + -0.632653061 = -0.887696456 Simplifying x + -0.632653061 = -0.887696456 Reorder the terms: -0.632653061 + x = -0.887696456 Solving -0.632653061 + x = -0.887696456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.632653061' to each side of the equation. -0.632653061 + 0.632653061 + x = -0.887696456 + 0.632653061 Combine like terms: -0.632653061 + 0.632653061 = 0.000000000 0.000000000 + x = -0.887696456 + 0.632653061 x = -0.887696456 + 0.632653061 Combine like terms: -0.887696456 + 0.632653061 = -0.255043395 x = -0.255043395 Simplifying x = -0.255043395Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.520349517, -0.255043395}
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