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Simplifying 4.9x2 + 1.9x + -3 = 0 Reorder the terms: -3 + 1.9x + 4.9x2 = 0 Solving -3 + 1.9x + 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'. -0.612244898 + 0.387755102x + x2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + 0.387755102x + 0.612244898 + x2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + 0.387755102x + x2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + 0.387755102x + x2 = 0 + 0.612244898 0.387755102x + x2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 0.387755102x + x2 = 0.612244898 The x term is 0.387755102x. Take half its coefficient (0.193877551). Square it (0.03758850478) and add it to both sides. Add '0.03758850478' to each side of the equation. 0.387755102x + 0.03758850478 + x2 = 0.612244898 + 0.03758850478 Reorder the terms: 0.03758850478 + 0.387755102x + x2 = 0.612244898 + 0.03758850478 Combine like terms: 0.612244898 + 0.03758850478 = 0.64983340278 0.03758850478 + 0.387755102x + x2 = 0.64983340278 Factor a perfect square on the left side: (x + 0.193877551)(x + 0.193877551) = 0.64983340278 Calculate the square root of the right side: 0.806122449 Break this problem into two subproblems by setting (x + 0.193877551) equal to 0.806122449 and -0.806122449.Subproblem 1
x + 0.193877551 = 0.806122449 Simplifying x + 0.193877551 = 0.806122449 Reorder the terms: 0.193877551 + x = 0.806122449 Solving 0.193877551 + x = 0.806122449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.193877551' to each side of the equation. 0.193877551 + -0.193877551 + x = 0.806122449 + -0.193877551 Combine like terms: 0.193877551 + -0.193877551 = 0.000000000 0.000000000 + x = 0.806122449 + -0.193877551 x = 0.806122449 + -0.193877551 Combine like terms: 0.806122449 + -0.193877551 = 0.612244898 x = 0.612244898 Simplifying x = 0.612244898Subproblem 2
x + 0.193877551 = -0.806122449 Simplifying x + 0.193877551 = -0.806122449 Reorder the terms: 0.193877551 + x = -0.806122449 Solving 0.193877551 + x = -0.806122449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.193877551' to each side of the equation. 0.193877551 + -0.193877551 + x = -0.806122449 + -0.193877551 Combine like terms: 0.193877551 + -0.193877551 = 0.000000000 0.000000000 + x = -0.806122449 + -0.193877551 x = -0.806122449 + -0.193877551 Combine like terms: -0.806122449 + -0.193877551 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.612244898, -1}
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