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Simplifying 10x2 + x + -32 = 0 Reorder the terms: -32 + x + 10x2 = 0 Solving -32 + x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3.2 + 0.1x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 0.1x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 0.1x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 0.1x + x2 = 0 + 3.2 0.1x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 0.1x + x2 = 3.2 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. 0.1x + 0.25 + x2 = 3.2 + 0.25 Reorder the terms: 0.25 + 0.1x + x2 = 3.2 + 0.25 Combine like terms: 3.2 + 0.25 = 3.45 0.25 + 0.1x + x2 = 3.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.45 Calculate the square root of the right side: 1.857417562 Break this problem into two subproblems by setting (x + 0.5) equal to 1.857417562 and -1.857417562.Subproblem 1
x + 0.5 = 1.857417562 Simplifying x + 0.5 = 1.857417562 Reorder the terms: 0.5 + x = 1.857417562 Solving 0.5 + x = 1.857417562 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 = 1.857417562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.857417562 + -0.5 x = 1.857417562 + -0.5 Combine like terms: 1.857417562 + -0.5 = 1.357417562 x = 1.357417562 Simplifying x = 1.357417562Subproblem 2
x + 0.5 = -1.857417562 Simplifying x + 0.5 = -1.857417562 Reorder the terms: 0.5 + x = -1.857417562 Solving 0.5 + x = -1.857417562 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 = -1.857417562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.857417562 + -0.5 x = -1.857417562 + -0.5 Combine like terms: -1.857417562 + -0.5 = -2.357417562 x = -2.357417562 Simplifying x = -2.357417562Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.357417562, -2.357417562}
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