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Simplifying 200 = 1.3x + 0.05x2 Solving 200 = 1.3x + 0.05x2 Solving for variable 'x'. Reorder the terms: 200 + -1.3x + -0.05x2 = 1.3x + -1.3x + 0.05x2 + -0.05x2 Combine like terms: 1.3x + -1.3x = 0.0 200 + -1.3x + -0.05x2 = 0.0 + 0.05x2 + -0.05x2 200 + -1.3x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 200 + -1.3x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -4000 + 26x + x2 = 0 Move the constant term to the right: Add '4000' to each side of the equation. -4000 + 26x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + 26x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + 26x + x2 = 0 + 4000 26x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 26x + x2 = 4000 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = 4000 + 169 Reorder the terms: 169 + 26x + x2 = 4000 + 169 Combine like terms: 4000 + 169 = 4169 169 + 26x + x2 = 4169 Factor a perfect square on the left side: (x + 13)(x + 13) = 4169 Calculate the square root of the right side: 64.567793829 Break this problem into two subproblems by setting (x + 13) equal to 64.567793829 and -64.567793829.Subproblem 1
x + 13 = 64.567793829 Simplifying x + 13 = 64.567793829 Reorder the terms: 13 + x = 64.567793829 Solving 13 + x = 64.567793829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 64.567793829 + -13 Combine like terms: 13 + -13 = 0 0 + x = 64.567793829 + -13 x = 64.567793829 + -13 Combine like terms: 64.567793829 + -13 = 51.567793829 x = 51.567793829 Simplifying x = 51.567793829Subproblem 2
x + 13 = -64.567793829 Simplifying x + 13 = -64.567793829 Reorder the terms: 13 + x = -64.567793829 Solving 13 + x = -64.567793829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -64.567793829 + -13 Combine like terms: 13 + -13 = 0 0 + x = -64.567793829 + -13 x = -64.567793829 + -13 Combine like terms: -64.567793829 + -13 = -77.567793829 x = -77.567793829 Simplifying x = -77.567793829Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.567793829, -77.567793829}
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