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Simplifying 10x = x2 + 3x + 2 Reorder the terms: 10x = 2 + 3x + x2 Solving 10x = 2 + 3x + x2 Solving for variable 'x'. Reorder the terms: -2 + 10x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2 Combine like terms: 10x + -3x = 7x -2 + 7x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2 Reorder the terms: -2 + 7x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2 Combine like terms: 2 + -2 = 0 -2 + 7x + -1x2 = 0 + 3x + -3x + x2 + -1x2 -2 + 7x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 -2 + 7x + -1x2 = 0 + x2 + -1x2 -2 + 7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -7x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -7x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -7x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x + x2 = 0 + -2 -7x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -7x + x2 = -2 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -2 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -2 + 12.25 Combine like terms: -2 + 12.25 = 10.25 12.25 + -7x + x2 = 10.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -3.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -3.5 = 3.201562119 Simplifying x + -3.5 = 3.201562119 Reorder the terms: -3.5 + x = 3.201562119 Solving -3.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.201562119 + 3.5 x = 3.201562119 + 3.5 Combine like terms: 3.201562119 + 3.5 = 6.701562119 x = 6.701562119 Simplifying x = 6.701562119Subproblem 2
x + -3.5 = -3.201562119 Simplifying x + -3.5 = -3.201562119 Reorder the terms: -3.5 + x = -3.201562119 Solving -3.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.201562119 + 3.5 x = -3.201562119 + 3.5 Combine like terms: -3.201562119 + 3.5 = 0.298437881 x = 0.298437881 Simplifying x = 0.298437881Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.701562119, 0.298437881}
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