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Simplifying 90x + -4.9x2 = -150 Solving 90x + -4.9x2 = -150 Solving for variable 'x'. Reorder the terms: 150 + 90x + -4.9x2 = -150 + 150 Combine like terms: -150 + 150 = 0 150 + 90x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -30.6122449 + -18.36734694x + x2 = 0 Move the constant term to the right: Add '30.6122449' to each side of the equation. -30.6122449 + -18.36734694x + 30.6122449 + x2 = 0 + 30.6122449 Reorder the terms: -30.6122449 + 30.6122449 + -18.36734694x + x2 = 0 + 30.6122449 Combine like terms: -30.6122449 + 30.6122449 = 0.0000000 0.0000000 + -18.36734694x + x2 = 0 + 30.6122449 -18.36734694x + x2 = 0 + 30.6122449 Combine like terms: 0 + 30.6122449 = 30.6122449 -18.36734694x + x2 = 30.6122449 The x term is -18.36734694x. Take half its coefficient (-9.18367347). Square it (84.33985840) and add it to both sides. Add '84.33985840' to each side of the equation. -18.36734694x + 84.33985840 + x2 = 30.6122449 + 84.33985840 Reorder the terms: 84.33985840 + -18.36734694x + x2 = 30.6122449 + 84.33985840 Combine like terms: 30.6122449 + 84.33985840 = 114.9521033 84.33985840 + -18.36734694x + x2 = 114.9521033 Factor a perfect square on the left side: (x + -9.18367347)(x + -9.18367347) = 114.9521033 Calculate the square root of the right side: 10.721571867 Break this problem into two subproblems by setting (x + -9.18367347) equal to 10.721571867 and -10.721571867.Subproblem 1
x + -9.18367347 = 10.721571867 Simplifying x + -9.18367347 = 10.721571867 Reorder the terms: -9.18367347 + x = 10.721571867 Solving -9.18367347 + x = 10.721571867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.18367347' to each side of the equation. -9.18367347 + 9.18367347 + x = 10.721571867 + 9.18367347 Combine like terms: -9.18367347 + 9.18367347 = 0.00000000 0.00000000 + x = 10.721571867 + 9.18367347 x = 10.721571867 + 9.18367347 Combine like terms: 10.721571867 + 9.18367347 = 19.905245337 x = 19.905245337 Simplifying x = 19.905245337Subproblem 2
x + -9.18367347 = -10.721571867 Simplifying x + -9.18367347 = -10.721571867 Reorder the terms: -9.18367347 + x = -10.721571867 Solving -9.18367347 + x = -10.721571867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.18367347' to each side of the equation. -9.18367347 + 9.18367347 + x = -10.721571867 + 9.18367347 Combine like terms: -9.18367347 + 9.18367347 = 0.00000000 0.00000000 + x = -10.721571867 + 9.18367347 x = -10.721571867 + 9.18367347 Combine like terms: -10.721571867 + 9.18367347 = -1.537898397 x = -1.537898397 Simplifying x = -1.537898397Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.905245337, -1.537898397}
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