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Simplifying 0.1x2 + -6x = -9 Reorder the terms: -6x + 0.1x2 = -9 Solving -6x + 0.1x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + -6x + 0.1x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -6x + 0.1x2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 90 + -60x + x2 = 0 Move the constant term to the right: Add '-90' to each side of the equation. 90 + -60x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -60x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -60x + x2 = 0 + -90 -60x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -60x + x2 = -90 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -90 + 900 Reorder the terms: 900 + -60x + x2 = -90 + 900 Combine like terms: -90 + 900 = 810 900 + -60x + x2 = 810 Factor a perfect square on the left side: (x + -30)(x + -30) = 810 Calculate the square root of the right side: 28.460498942 Break this problem into two subproblems by setting (x + -30) equal to 28.460498942 and -28.460498942.Subproblem 1
x + -30 = 28.460498942 Simplifying x + -30 = 28.460498942 Reorder the terms: -30 + x = 28.460498942 Solving -30 + x = 28.460498942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 28.460498942 + 30 Combine like terms: -30 + 30 = 0 0 + x = 28.460498942 + 30 x = 28.460498942 + 30 Combine like terms: 28.460498942 + 30 = 58.460498942 x = 58.460498942 Simplifying x = 58.460498942Subproblem 2
x + -30 = -28.460498942 Simplifying x + -30 = -28.460498942 Reorder the terms: -30 + x = -28.460498942 Solving -30 + x = -28.460498942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -28.460498942 + 30 Combine like terms: -30 + 30 = 0 0 + x = -28.460498942 + 30 x = -28.460498942 + 30 Combine like terms: -28.460498942 + 30 = 1.539501058 x = 1.539501058 Simplifying x = 1.539501058Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.460498942, 1.539501058}
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