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Simplifying -4.9x2 + 3x + 250 = 0 Reorder the terms: 250 + 3x + -4.9x2 = 0 Solving 250 + 3x + -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'. -51.02040816 + -0.612244898x + x2 = 0 Move the constant term to the right: Add '51.02040816' to each side of the equation. -51.02040816 + -0.612244898x + 51.02040816 + x2 = 0 + 51.02040816 Reorder the terms: -51.02040816 + 51.02040816 + -0.612244898x + x2 = 0 + 51.02040816 Combine like terms: -51.02040816 + 51.02040816 = 0.00000000 0.00000000 + -0.612244898x + x2 = 0 + 51.02040816 -0.612244898x + x2 = 0 + 51.02040816 Combine like terms: 0 + 51.02040816 = 51.02040816 -0.612244898x + x2 = 51.02040816 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 = 51.02040816 + 0.09371095378 Reorder the terms: 0.09371095378 + -0.612244898x + x2 = 51.02040816 + 0.09371095378 Combine like terms: 51.02040816 + 0.09371095378 = 51.11411911378 0.09371095378 + -0.612244898x + x2 = 51.11411911378 Factor a perfect square on the left side: (x + -0.306122449)(x + -0.306122449) = 51.11411911378 Calculate the square root of the right side: 7.1494139 Break this problem into two subproblems by setting (x + -0.306122449) equal to 7.1494139 and -7.1494139.Subproblem 1
x + -0.306122449 = 7.1494139 Simplifying x + -0.306122449 = 7.1494139 Reorder the terms: -0.306122449 + x = 7.1494139 Solving -0.306122449 + x = 7.1494139 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 = 7.1494139 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + x = 7.1494139 + 0.306122449 x = 7.1494139 + 0.306122449 Combine like terms: 7.1494139 + 0.306122449 = 7.455536349 x = 7.455536349 Simplifying x = 7.455536349Subproblem 2
x + -0.306122449 = -7.1494139 Simplifying x + -0.306122449 = -7.1494139 Reorder the terms: -0.306122449 + x = -7.1494139 Solving -0.306122449 + x = -7.1494139 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 = -7.1494139 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + x = -7.1494139 + 0.306122449 x = -7.1494139 + 0.306122449 Combine like terms: -7.1494139 + 0.306122449 = -6.843291451 x = -6.843291451 Simplifying x = -6.843291451Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.455536349, -6.843291451}
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