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Simplifying 4.69 = 0.0065x2 + -0.2x Reorder the terms: 4.69 = -0.2x + 0.0065x2 Solving 4.69 = -0.2x + 0.0065x2 Solving for variable 'x'. Reorder the terms: 4.69 + 0.2x + -0.0065x2 = -0.2x + 0.2x + 0.0065x2 + -0.0065x2 Combine like terms: -0.2x + 0.2x = 0.0 4.69 + 0.2x + -0.0065x2 = 0.0 + 0.0065x2 + -0.0065x2 4.69 + 0.2x + -0.0065x2 = 0.0065x2 + -0.0065x2 Combine like terms: 0.0065x2 + -0.0065x2 = 0.0000 4.69 + 0.2x + -0.0065x2 = 0.0000 Begin completing the square. Divide all terms by -0.0065 the coefficient of the squared term: Divide each side by '-0.0065'. -721.5384615 + -30.76923077x + x2 = 0 Move the constant term to the right: Add '721.5384615' to each side of the equation. -721.5384615 + -30.76923077x + 721.5384615 + x2 = 0 + 721.5384615 Reorder the terms: -721.5384615 + 721.5384615 + -30.76923077x + x2 = 0 + 721.5384615 Combine like terms: -721.5384615 + 721.5384615 = 0.0000000 0.0000000 + -30.76923077x + x2 = 0 + 721.5384615 -30.76923077x + x2 = 0 + 721.5384615 Combine like terms: 0 + 721.5384615 = 721.5384615 -30.76923077x + x2 = 721.5384615 The x term is -30.76923077x. Take half its coefficient (-15.38461539). Square it (236.6863907) and add it to both sides. Add '236.6863907' to each side of the equation. -30.76923077x + 236.6863907 + x2 = 721.5384615 + 236.6863907 Reorder the terms: 236.6863907 + -30.76923077x + x2 = 721.5384615 + 236.6863907 Combine like terms: 721.5384615 + 236.6863907 = 958.2248522 236.6863907 + -30.76923077x + x2 = 958.2248522 Factor a perfect square on the left side: (x + -15.38461539)(x + -15.38461539) = 958.2248522 Calculate the square root of the right side: 30.95520719 Break this problem into two subproblems by setting (x + -15.38461539) equal to 30.95520719 and -30.95520719.Subproblem 1
x + -15.38461539 = 30.95520719 Simplifying x + -15.38461539 = 30.95520719 Reorder the terms: -15.38461539 + x = 30.95520719 Solving -15.38461539 + x = 30.95520719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.38461539' to each side of the equation. -15.38461539 + 15.38461539 + x = 30.95520719 + 15.38461539 Combine like terms: -15.38461539 + 15.38461539 = 0.00000000 0.00000000 + x = 30.95520719 + 15.38461539 x = 30.95520719 + 15.38461539 Combine like terms: 30.95520719 + 15.38461539 = 46.33982258 x = 46.33982258 Simplifying x = 46.33982258Subproblem 2
x + -15.38461539 = -30.95520719 Simplifying x + -15.38461539 = -30.95520719 Reorder the terms: -15.38461539 + x = -30.95520719 Solving -15.38461539 + x = -30.95520719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.38461539' to each side of the equation. -15.38461539 + 15.38461539 + x = -30.95520719 + 15.38461539 Combine like terms: -15.38461539 + 15.38461539 = 0.00000000 0.00000000 + x = -30.95520719 + 15.38461539 x = -30.95520719 + 15.38461539 Combine like terms: -30.95520719 + 15.38461539 = -15.5705918 x = -15.5705918 Simplifying x = -15.5705918Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.33982258, -15.5705918}
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