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Simplifying 0 = -4.9x2 + 3x + 100 Reorder the terms: 0 = 100 + 3x + -4.9x2 Solving 0 = 100 + 3x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + -3x + 4.9x2 = 100 + 3x + -4.9x2 + -100 + -3x + 4.9x2 Reorder the terms: -100 + -3x + 4.9x2 = 100 + -100 + 3x + -3x + -4.9x2 + 4.9x2 Combine like terms: 100 + -100 = 0 -100 + -3x + 4.9x2 = 0 + 3x + -3x + -4.9x2 + 4.9x2 -100 + -3x + 4.9x2 = 3x + -3x + -4.9x2 + 4.9x2 Combine like terms: 3x + -3x = 0 -100 + -3x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -100 + -3x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -100 + -3x + 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'. -20.40816327 + -0.612244898x + x2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + -0.612244898x + 20.40816327 + x2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + -0.612244898x + x2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + -0.612244898x + x2 = 0 + 20.40816327 -0.612244898x + x2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 -0.612244898x + x2 = 20.40816327 The x term is -0.612244898x. Take half its coefficient (-0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. -0.612244898x + 0.09371095378 + x2 = 20.40816327 + 0.09371095378 Reorder the terms: 0.09371095378 + -0.612244898x + x2 = 20.40816327 + 0.09371095378 Combine like terms: 20.40816327 + 0.09371095378 = 20.50187422378 0.09371095378 + -0.612244898x + x2 = 20.50187422378 Factor a perfect square on the left side: (x + -0.306122449)(x + -0.306122449) = 20.50187422378 Calculate the square root of the right side: 4.527899538 Break this problem into two subproblems by setting (x + -0.306122449) equal to 4.527899538 and -4.527899538.Subproblem 1
x + -0.306122449 = 4.527899538 Simplifying x + -0.306122449 = 4.527899538 Reorder the terms: -0.306122449 + x = 4.527899538 Solving -0.306122449 + x = 4.527899538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.306122449' to each side of the equation. -0.306122449 + 0.306122449 + x = 4.527899538 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + x = 4.527899538 + 0.306122449 x = 4.527899538 + 0.306122449 Combine like terms: 4.527899538 + 0.306122449 = 4.834021987 x = 4.834021987 Simplifying x = 4.834021987Subproblem 2
x + -0.306122449 = -4.527899538 Simplifying x + -0.306122449 = -4.527899538 Reorder the terms: -0.306122449 + x = -4.527899538 Solving -0.306122449 + x = -4.527899538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.306122449' to each side of the equation. -0.306122449 + 0.306122449 + x = -4.527899538 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + x = -4.527899538 + 0.306122449 x = -4.527899538 + 0.306122449 Combine like terms: -4.527899538 + 0.306122449 = -4.221777089 x = -4.221777089 Simplifying x = -4.221777089Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.834021987, -4.221777089}
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