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Simplifying -4.9x2 + 103x + 199 = 0 Reorder the terms: 199 + 103x + -4.9x2 = 0 Solving 199 + 103x + -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'. -40.6122449 + -21.02040816x + x2 = 0 Move the constant term to the right: Add '40.6122449' to each side of the equation. -40.6122449 + -21.02040816x + 40.6122449 + x2 = 0 + 40.6122449 Reorder the terms: -40.6122449 + 40.6122449 + -21.02040816x + x2 = 0 + 40.6122449 Combine like terms: -40.6122449 + 40.6122449 = 0.0000000 0.0000000 + -21.02040816x + x2 = 0 + 40.6122449 -21.02040816x + x2 = 0 + 40.6122449 Combine like terms: 0 + 40.6122449 = 40.6122449 -21.02040816x + x2 = 40.6122449 The x term is -21.02040816x. Take half its coefficient (-10.51020408). Square it (110.4643898) and add it to both sides. Add '110.4643898' to each side of the equation. -21.02040816x + 110.4643898 + x2 = 40.6122449 + 110.4643898 Reorder the terms: 110.4643898 + -21.02040816x + x2 = 40.6122449 + 110.4643898 Combine like terms: 40.6122449 + 110.4643898 = 151.0766347 110.4643898 + -21.02040816x + x2 = 151.0766347 Factor a perfect square on the left side: (x + -10.51020408)(x + -10.51020408) = 151.0766347 Calculate the square root of the right side: 12.291323554 Break this problem into two subproblems by setting (x + -10.51020408) equal to 12.291323554 and -12.291323554.Subproblem 1
x + -10.51020408 = 12.291323554 Simplifying x + -10.51020408 = 12.291323554 Reorder the terms: -10.51020408 + x = 12.291323554 Solving -10.51020408 + x = 12.291323554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.51020408' to each side of the equation. -10.51020408 + 10.51020408 + x = 12.291323554 + 10.51020408 Combine like terms: -10.51020408 + 10.51020408 = 0.00000000 0.00000000 + x = 12.291323554 + 10.51020408 x = 12.291323554 + 10.51020408 Combine like terms: 12.291323554 + 10.51020408 = 22.801527634 x = 22.801527634 Simplifying x = 22.801527634Subproblem 2
x + -10.51020408 = -12.291323554 Simplifying x + -10.51020408 = -12.291323554 Reorder the terms: -10.51020408 + x = -12.291323554 Solving -10.51020408 + x = -12.291323554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.51020408' to each side of the equation. -10.51020408 + 10.51020408 + x = -12.291323554 + 10.51020408 Combine like terms: -10.51020408 + 10.51020408 = 0.00000000 0.00000000 + x = -12.291323554 + 10.51020408 x = -12.291323554 + 10.51020408 Combine like terms: -12.291323554 + 10.51020408 = -1.781119474 x = -1.781119474 Simplifying x = -1.781119474Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.801527634, -1.781119474}
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