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Simplifying 2 = -0.05x2 + 0.7x Reorder the terms: 2 = 0.7x + -0.05x2 Solving 2 = 0.7x + -0.05x2 Solving for variable 'x'. Reorder the terms: 2 + -0.7x + 0.05x2 = 0.7x + -0.7x + -0.05x2 + 0.05x2 Combine like terms: 0.7x + -0.7x = 0.0 2 + -0.7x + 0.05x2 = 0.0 + -0.05x2 + 0.05x2 2 + -0.7x + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 2 + -0.7x + 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'. 40 + -14x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -14x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -14x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -14x + x2 = 0 + -40 -14x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -14x + x2 = -40 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -40 + 49 Reorder the terms: 49 + -14x + x2 = -40 + 49 Combine like terms: -40 + 49 = 9 49 + -14x + x2 = 9 Factor a perfect square on the left side: (x + -7)(x + -7) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + -7) equal to 3 and -3.Subproblem 1
x + -7 = 3 Simplifying x + -7 = 3 Reorder the terms: -7 + x = 3 Solving -7 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 3 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3 + 7 x = 3 + 7 Combine like terms: 3 + 7 = 10 x = 10 Simplifying x = 10Subproblem 2
x + -7 = -3 Simplifying x + -7 = -3 Reorder the terms: -7 + x = -3 Solving -7 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -3 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3 + 7 x = -3 + 7 Combine like terms: -3 + 7 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, 4}
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