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Simplifying 0 = 23 + 13x + -4.9x2 Solving 0 = 23 + 13x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -23 = -23 -23 + -13x + 4.9x2 = 23 + 13x + -4.9x2 + -23 + -13x + 4.9x2 Reorder the terms: -23 + -13x + 4.9x2 = 23 + -23 + 13x + -13x + -4.9x2 + 4.9x2 Combine like terms: 23 + -23 = 0 -23 + -13x + 4.9x2 = 0 + 13x + -13x + -4.9x2 + 4.9x2 -23 + -13x + 4.9x2 = 13x + -13x + -4.9x2 + 4.9x2 Combine like terms: 13x + -13x = 0 -23 + -13x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -23 + -13x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -23 + -13x + 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'. -4.693877551 + -2.653061224x + x2 = 0 Move the constant term to the right: Add '4.693877551' to each side of the equation. -4.693877551 + -2.653061224x + 4.693877551 + x2 = 0 + 4.693877551 Reorder the terms: -4.693877551 + 4.693877551 + -2.653061224x + x2 = 0 + 4.693877551 Combine like terms: -4.693877551 + 4.693877551 = 0.000000000 0.000000000 + -2.653061224x + x2 = 0 + 4.693877551 -2.653061224x + x2 = 0 + 4.693877551 Combine like terms: 0 + 4.693877551 = 4.693877551 -2.653061224x + x2 = 4.693877551 The x term is -2.653061224x. Take half its coefficient (-1.326530612). Square it (1.759683465) and add it to both sides. Add '1.759683465' to each side of the equation. -2.653061224x + 1.759683465 + x2 = 4.693877551 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224x + x2 = 4.693877551 + 1.759683465 Combine like terms: 4.693877551 + 1.759683465 = 6.453561016 1.759683465 + -2.653061224x + x2 = 6.453561016 Factor a perfect square on the left side: (x + -1.326530612)(x + -1.326530612) = 6.453561016 Calculate the square root of the right side: 2.540385997 Break this problem into two subproblems by setting (x + -1.326530612) equal to 2.540385997 and -2.540385997.Subproblem 1
x + -1.326530612 = 2.540385997 Simplifying x + -1.326530612 = 2.540385997 Reorder the terms: -1.326530612 + x = 2.540385997 Solving -1.326530612 + x = 2.540385997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + x = 2.540385997 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + x = 2.540385997 + 1.326530612 x = 2.540385997 + 1.326530612 Combine like terms: 2.540385997 + 1.326530612 = 3.866916609 x = 3.866916609 Simplifying x = 3.866916609Subproblem 2
x + -1.326530612 = -2.540385997 Simplifying x + -1.326530612 = -2.540385997 Reorder the terms: -1.326530612 + x = -2.540385997 Solving -1.326530612 + x = -2.540385997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + x = -2.540385997 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + x = -2.540385997 + 1.326530612 x = -2.540385997 + 1.326530612 Combine like terms: -2.540385997 + 1.326530612 = -1.213855385 x = -1.213855385 Simplifying x = -1.213855385Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.866916609, -1.213855385}
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