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Simplifying 1100 = 28x + 0.3x2 Solving 1100 = 28x + 0.3x2 Solving for variable 'x'. Reorder the terms: 1100 + -28x + -0.3x2 = 28x + -28x + 0.3x2 + -0.3x2 Combine like terms: 28x + -28x = 0 1100 + -28x + -0.3x2 = 0 + 0.3x2 + -0.3x2 1100 + -28x + -0.3x2 = 0.3x2 + -0.3x2 Combine like terms: 0.3x2 + -0.3x2 = 0.0 1100 + -28x + -0.3x2 = 0.0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -3666.666667 + 93.33333333x + x2 = 0 Move the constant term to the right: Add '3666.666667' to each side of the equation. -3666.666667 + 93.33333333x + 3666.666667 + x2 = 0 + 3666.666667 Reorder the terms: -3666.666667 + 3666.666667 + 93.33333333x + x2 = 0 + 3666.666667 Combine like terms: -3666.666667 + 3666.666667 = 0.000000 0.000000 + 93.33333333x + x2 = 0 + 3666.666667 93.33333333x + x2 = 0 + 3666.666667 Combine like terms: 0 + 3666.666667 = 3666.666667 93.33333333x + x2 = 3666.666667 The x term is 93.33333333x. Take half its coefficient (46.66666667). Square it (2177.777778) and add it to both sides. Add '2177.777778' to each side of the equation. 93.33333333x + 2177.777778 + x2 = 3666.666667 + 2177.777778 Reorder the terms: 2177.777778 + 93.33333333x + x2 = 3666.666667 + 2177.777778 Combine like terms: 3666.666667 + 2177.777778 = 5844.444445 2177.777778 + 93.33333333x + x2 = 5844.444445 Factor a perfect square on the left side: (x + 46.66666667)(x + 46.66666667) = 5844.444445 Calculate the square root of the right side: 76.448966278 Break this problem into two subproblems by setting (x + 46.66666667) equal to 76.448966278 and -76.448966278.Subproblem 1
x + 46.66666667 = 76.448966278 Simplifying x + 46.66666667 = 76.448966278 Reorder the terms: 46.66666667 + x = 76.448966278 Solving 46.66666667 + x = 76.448966278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46.66666667' to each side of the equation. 46.66666667 + -46.66666667 + x = 76.448966278 + -46.66666667 Combine like terms: 46.66666667 + -46.66666667 = 0.00000000 0.00000000 + x = 76.448966278 + -46.66666667 x = 76.448966278 + -46.66666667 Combine like terms: 76.448966278 + -46.66666667 = 29.782299608 x = 29.782299608 Simplifying x = 29.782299608Subproblem 2
x + 46.66666667 = -76.448966278 Simplifying x + 46.66666667 = -76.448966278 Reorder the terms: 46.66666667 + x = -76.448966278 Solving 46.66666667 + x = -76.448966278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46.66666667' to each side of the equation. 46.66666667 + -46.66666667 + x = -76.448966278 + -46.66666667 Combine like terms: 46.66666667 + -46.66666667 = 0.00000000 0.00000000 + x = -76.448966278 + -46.66666667 x = -76.448966278 + -46.66666667 Combine like terms: -76.448966278 + -46.66666667 = -123.115632948 x = -123.115632948 Simplifying x = -123.115632948Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.782299608, -123.115632948}
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