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Simplifying 5x2 + -70x + 214 = 0 Reorder the terms: 214 + -70x + 5x2 = 0 Solving 214 + -70x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 42.8 + -14x + x2 = 0 Move the constant term to the right: Add '-42.8' to each side of the equation. 42.8 + -14x + -42.8 + x2 = 0 + -42.8 Reorder the terms: 42.8 + -42.8 + -14x + x2 = 0 + -42.8 Combine like terms: 42.8 + -42.8 = 0.0 0.0 + -14x + x2 = 0 + -42.8 -14x + x2 = 0 + -42.8 Combine like terms: 0 + -42.8 = -42.8 -14x + x2 = -42.8 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 = -42.8 + 49 Reorder the terms: 49 + -14x + x2 = -42.8 + 49 Combine like terms: -42.8 + 49 = 6.2 49 + -14x + x2 = 6.2 Factor a perfect square on the left side: (x + -7)(x + -7) = 6.2 Calculate the square root of the right side: 2.48997992 Break this problem into two subproblems by setting (x + -7) equal to 2.48997992 and -2.48997992.Subproblem 1
x + -7 = 2.48997992 Simplifying x + -7 = 2.48997992 Reorder the terms: -7 + x = 2.48997992 Solving -7 + x = 2.48997992 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 = 2.48997992 + 7 Combine like terms: -7 + 7 = 0 0 + x = 2.48997992 + 7 x = 2.48997992 + 7 Combine like terms: 2.48997992 + 7 = 9.48997992 x = 9.48997992 Simplifying x = 9.48997992Subproblem 2
x + -7 = -2.48997992 Simplifying x + -7 = -2.48997992 Reorder the terms: -7 + x = -2.48997992 Solving -7 + x = -2.48997992 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 = -2.48997992 + 7 Combine like terms: -7 + 7 = 0 0 + x = -2.48997992 + 7 x = -2.48997992 + 7 Combine like terms: -2.48997992 + 7 = 4.51002008 x = 4.51002008 Simplifying x = 4.51002008Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.48997992, 4.51002008}
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