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Simplifying (4 + 5) * 5 = (x + 4 + x + -2) * x + -2 Combine like terms: 4 + 5 = 9 (9) * 5 = (x + 4 + x + -2) * x + -2 Multiply 9 * 5 45 = (x + 4 + x + -2) * x + -2 Reorder the terms: 45 = (4 + -2 + x + x) * x + -2 Combine like terms: 4 + -2 = 2 45 = (2 + x + x) * x + -2 Combine like terms: x + x = 2x 45 = (2 + 2x) * x + -2 Reorder the terms for easier multiplication: 45 = x(2 + 2x) + -2 45 = (2 * x + 2x * x) + -2 45 = (2x + 2x2) + -2 Reorder the terms: 45 = -2 + 2x + 2x2 Solving 45 = -2 + 2x + 2x2 Solving for variable 'x'. Combine like terms: 45 + 2 = 47 47 + -2x + -2x2 = -2 + 2x + 2x2 + 2 + -2x + -2x2 Reorder the terms: 47 + -2x + -2x2 = -2 + 2 + 2x + -2x + 2x2 + -2x2 Combine like terms: -2 + 2 = 0 47 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2 47 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 47 + -2x + -2x2 = 0 + 2x2 + -2x2 47 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 47 + -2x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -23.5 + x + x2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + x + 23.5 + x2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + x + x2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x + x2 = 0 + 23.5 x + x2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 x + x2 = 23.5 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 = 23.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 23.5 + 0.25 Combine like terms: 23.5 + 0.25 = 23.75 1.25 + x2 = 23.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 23.75 Calculate the square root of the right side: 4.873397172 Break this problem into two subproblems by setting (x + 0.5) equal to 4.873397172 and -4.873397172.Subproblem 1
x + 0.5 = 4.873397172 Simplifying x + 0.5 = 4.873397172 Reorder the terms: 0.5 + x = 4.873397172 Solving 0.5 + x = 4.873397172 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 = 4.873397172 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.873397172 + -0.5 x = 4.873397172 + -0.5 Combine like terms: 4.873397172 + -0.5 = 4.373397172 x = 4.373397172 Simplifying x = 4.373397172Subproblem 2
x + 0.5 = -4.873397172 Simplifying x + 0.5 = -4.873397172 Reorder the terms: 0.5 + x = -4.873397172 Solving 0.5 + x = -4.873397172 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 = -4.873397172 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.873397172 + -0.5 x = -4.873397172 + -0.5 Combine like terms: -4.873397172 + -0.5 = -5.373397172 x = -5.373397172 Simplifying x = -5.373397172Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.373397172, -5.373397172}
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