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Simplifying 0.05x2 + 0.97x + 0.26 = 300 Reorder the terms: 0.26 + 0.97x + 0.05x2 = 300 Solving 0.26 + 0.97x + 0.05x2 = 300 Solving for variable 'x'. Reorder the terms: 0.26 + -300 + 0.97x + 0.05x2 = 300 + -300 Combine like terms: 0.26 + -300 = -299.74 -299.74 + 0.97x + 0.05x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -299.74 + 0.97x + 0.05x2 = 0 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -5994.8 + 19.4x + x2 = 0 Move the constant term to the right: Add '5994.8' to each side of the equation. -5994.8 + 19.4x + 5994.8 + x2 = 0 + 5994.8 Reorder the terms: -5994.8 + 5994.8 + 19.4x + x2 = 0 + 5994.8 Combine like terms: -5994.8 + 5994.8 = 0.0 0.0 + 19.4x + x2 = 0 + 5994.8 19.4x + x2 = 0 + 5994.8 Combine like terms: 0 + 5994.8 = 5994.8 19.4x + x2 = 5994.8 The x term is 19.4x. Take half its coefficient (9.7). Square it (94.09) and add it to both sides. Add '94.09' to each side of the equation. 19.4x + 94.09 + x2 = 5994.8 + 94.09 Reorder the terms: 94.09 + 19.4x + x2 = 5994.8 + 94.09 Combine like terms: 5994.8 + 94.09 = 6088.89 94.09 + 19.4x + x2 = 6088.89 Factor a perfect square on the left side: (x + 9.7)(x + 9.7) = 6088.89 Calculate the square root of the right side: 78.031339858 Break this problem into two subproblems by setting (x + 9.7) equal to 78.031339858 and -78.031339858.Subproblem 1
x + 9.7 = 78.031339858 Simplifying x + 9.7 = 78.031339858 Reorder the terms: 9.7 + x = 78.031339858 Solving 9.7 + x = 78.031339858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.7' to each side of the equation. 9.7 + -9.7 + x = 78.031339858 + -9.7 Combine like terms: 9.7 + -9.7 = 0.0 0.0 + x = 78.031339858 + -9.7 x = 78.031339858 + -9.7 Combine like terms: 78.031339858 + -9.7 = 68.331339858 x = 68.331339858 Simplifying x = 68.331339858Subproblem 2
x + 9.7 = -78.031339858 Simplifying x + 9.7 = -78.031339858 Reorder the terms: 9.7 + x = -78.031339858 Solving 9.7 + x = -78.031339858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.7' to each side of the equation. 9.7 + -9.7 + x = -78.031339858 + -9.7 Combine like terms: 9.7 + -9.7 = 0.0 0.0 + x = -78.031339858 + -9.7 x = -78.031339858 + -9.7 Combine like terms: -78.031339858 + -9.7 = -87.731339858 x = -87.731339858 Simplifying x = -87.731339858Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.331339858, -87.731339858}
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