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Simplifying 20 = -5x2 + 30.5x Reorder the terms: 20 = 30.5x + -5x2 Solving 20 = 30.5x + -5x2 Solving for variable 'x'. Reorder the terms: 20 + -30.5x + 5x2 = 30.5x + -30.5x + -5x2 + 5x2 Combine like terms: 30.5x + -30.5x = 0.0 20 + -30.5x + 5x2 = 0.0 + -5x2 + 5x2 20 + -30.5x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 20 + -30.5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + -6.1x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6.1x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -6.1x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6.1x + x2 = 0 + -4 -6.1x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6.1x + x2 = -4 The x term is -6.1x. Take half its coefficient (-3.05). Square it (9.3025) and add it to both sides. Add '9.3025' to each side of the equation. -6.1x + 9.3025 + x2 = -4 + 9.3025 Reorder the terms: 9.3025 + -6.1x + x2 = -4 + 9.3025 Combine like terms: -4 + 9.3025 = 5.3025 9.3025 + -6.1x + x2 = 5.3025 Factor a perfect square on the left side: (x + -3.05)(x + -3.05) = 5.3025 Calculate the square root of the right side: 2.302715788 Break this problem into two subproblems by setting (x + -3.05) equal to 2.302715788 and -2.302715788.Subproblem 1
x + -3.05 = 2.302715788 Simplifying x + -3.05 = 2.302715788 Reorder the terms: -3.05 + x = 2.302715788 Solving -3.05 + x = 2.302715788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.05' to each side of the equation. -3.05 + 3.05 + x = 2.302715788 + 3.05 Combine like terms: -3.05 + 3.05 = 0.00 0.00 + x = 2.302715788 + 3.05 x = 2.302715788 + 3.05 Combine like terms: 2.302715788 + 3.05 = 5.352715788 x = 5.352715788 Simplifying x = 5.352715788Subproblem 2
x + -3.05 = -2.302715788 Simplifying x + -3.05 = -2.302715788 Reorder the terms: -3.05 + x = -2.302715788 Solving -3.05 + x = -2.302715788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.05' to each side of the equation. -3.05 + 3.05 + x = -2.302715788 + 3.05 Combine like terms: -3.05 + 3.05 = 0.00 0.00 + x = -2.302715788 + 3.05 x = -2.302715788 + 3.05 Combine like terms: -2.302715788 + 3.05 = 0.747284212 x = 0.747284212 Simplifying x = 0.747284212Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.352715788, 0.747284212}
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