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Simplifying 5x2 + -2 + 5x + -5 = 0 Reorder the terms: -2 + -5 + 5x + 5x2 = 0 Combine like terms: -2 + -5 = -7 -7 + 5x + 5x2 = 0 Solving -7 + 5x + 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'. -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 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 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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