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Simplifying 0.07x + 0.01(70) = 0.05x(x + 70) Multiply 0.01 * 70 0.07x + 0.7 = 0.05x(x + 70) Reorder the terms: 0.7 + 0.07x = 0.05x(x + 70) Reorder the terms: 0.7 + 0.07x = 0.05x(70 + x) 0.7 + 0.07x = (70 * 0.05x + x * 0.05x) 0.7 + 0.07x = (3.5x + 0.05x2) Solving 0.7 + 0.07x = 3.5x + 0.05x2 Solving for variable 'x'. Combine like terms: 0.07x + -3.5x = -3.43x 0.7 + -3.43x + -0.05x2 = 3.5x + 0.05x2 + -3.5x + -0.05x2 Reorder the terms: 0.7 + -3.43x + -0.05x2 = 3.5x + -3.5x + 0.05x2 + -0.05x2 Combine like terms: 3.5x + -3.5x = 0.0 0.7 + -3.43x + -0.05x2 = 0.0 + 0.05x2 + -0.05x2 0.7 + -3.43x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 0.7 + -3.43x + -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'. -14 + 68.6x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 68.6x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 68.6x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 68.6x + x2 = 0 + 14 68.6x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 68.6x + x2 = 14 The x term is 68.6x. Take half its coefficient (34.3). Square it (1176.49) and add it to both sides. Add '1176.49' to each side of the equation. 68.6x + 1176.49 + x2 = 14 + 1176.49 Reorder the terms: 1176.49 + 68.6x + x2 = 14 + 1176.49 Combine like terms: 14 + 1176.49 = 1190.49 1176.49 + 68.6x + x2 = 1190.49 Factor a perfect square on the left side: (x + 34.3)(x + 34.3) = 1190.49 Calculate the square root of the right side: 34.503478086 Break this problem into two subproblems by setting (x + 34.3) equal to 34.503478086 and -34.503478086.Subproblem 1
x + 34.3 = 34.503478086 Simplifying x + 34.3 = 34.503478086 Reorder the terms: 34.3 + x = 34.503478086 Solving 34.3 + x = 34.503478086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.3' to each side of the equation. 34.3 + -34.3 + x = 34.503478086 + -34.3 Combine like terms: 34.3 + -34.3 = 0.0 0.0 + x = 34.503478086 + -34.3 x = 34.503478086 + -34.3 Combine like terms: 34.503478086 + -34.3 = 0.203478086 x = 0.203478086 Simplifying x = 0.203478086Subproblem 2
x + 34.3 = -34.503478086 Simplifying x + 34.3 = -34.503478086 Reorder the terms: 34.3 + x = -34.503478086 Solving 34.3 + x = -34.503478086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.3' to each side of the equation. 34.3 + -34.3 + x = -34.503478086 + -34.3 Combine like terms: 34.3 + -34.3 = 0.0 0.0 + x = -34.503478086 + -34.3 x = -34.503478086 + -34.3 Combine like terms: -34.503478086 + -34.3 = -68.803478086 x = -68.803478086 Simplifying x = -68.803478086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.203478086, -68.803478086}
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