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Simplifying (5x2) = 7 + -5x Solving (5x2) = 7 + -5x Solving for variable 'x'. Reorder the terms: -7 + 5x + (5x2) = 7 + -5x + -7 + 5x Reorder the terms: -7 + 5x + (5x2) = 7 + -7 + -5x + 5x Combine like terms: 7 + -7 = 0 -7 + 5x + (5x2) = 0 + -5x + 5x -7 + 5x + (5x2) = -5x + 5x Combine like terms: -5x + 5x = 0 -7 + 5x + (5x2) = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x + x2 = 0 + 1.4 x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 x + x2 = 1.4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.4 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.4 + 0.25 Combine like terms: 1.4 + 0.25 = 1.65 1.25 + x2 = 1.65 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 1.65 Calculate the square root of the right side: 1.284523258 Break this problem into two subproblems by setting ((x) + 0.5) equal to 1.284523258 and -1.284523258.Subproblem 1
(x) + 0.5 = 1.284523258 Simplifying (x) + 0.5 = 1.284523258 x + 0.5 = 1.284523258 Reorder the terms: 0.5 + x = 1.284523258 Solving 0.5 + x = 1.284523258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.284523258 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.284523258 + -0.5 x = 1.284523258 + -0.5 Combine like terms: 1.284523258 + -0.5 = 0.784523258 x = 0.784523258 Simplifying x = 0.784523258Subproblem 2
(x) + 0.5 = -1.284523258 Simplifying (x) + 0.5 = -1.284523258 x + 0.5 = -1.284523258 Reorder the terms: 0.5 + x = -1.284523258 Solving 0.5 + x = -1.284523258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.284523258 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.284523258 + -0.5 x = -1.284523258 + -0.5 Combine like terms: -1.284523258 + -0.5 = -1.784523258 x = -1.784523258 Simplifying x = -1.784523258Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.784523258, -1.784523258}
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