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Simplifying 10x2 + x = 6.2 Reorder the terms: x + 10x2 = 6.2 Solving x + 10x2 = 6.2 Solving for variable 'x'. Reorder the terms: -6.2 + x + 10x2 = 6.2 + -6.2 Combine like terms: 6.2 + -6.2 = 0.0 -6.2 + x + 10x2 = 0.0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.62 + 0.1x + x2 = 0.0 Move the constant term to the right: Add '0.62' to each side of the equation. -0.62 + 0.1x + 0.62 + x2 = 0.0 + 0.62 Reorder the terms: -0.62 + 0.62 + 0.1x + x2 = 0.0 + 0.62 Combine like terms: -0.62 + 0.62 = 0.00 0.00 + 0.1x + x2 = 0.0 + 0.62 0.1x + x2 = 0.0 + 0.62 Combine like terms: 0.0 + 0.62 = 0.62 0.1x + x2 = 0.62 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 = 0.62 + 0.25 Reorder the terms: 0.25 + 0.1x + x2 = 0.62 + 0.25 Combine like terms: 0.62 + 0.25 = 0.87 0.25 + 0.1x + x2 = 0.87 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.87 Calculate the square root of the right side: 0.932737905 Break this problem into two subproblems by setting (x + 0.5) equal to 0.932737905 and -0.932737905.Subproblem 1
x + 0.5 = 0.932737905 Simplifying x + 0.5 = 0.932737905 Reorder the terms: 0.5 + x = 0.932737905 Solving 0.5 + x = 0.932737905 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 = 0.932737905 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.932737905 + -0.5 x = 0.932737905 + -0.5 Combine like terms: 0.932737905 + -0.5 = 0.432737905 x = 0.432737905 Simplifying x = 0.432737905Subproblem 2
x + 0.5 = -0.932737905 Simplifying x + 0.5 = -0.932737905 Reorder the terms: 0.5 + x = -0.932737905 Solving 0.5 + x = -0.932737905 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 = -0.932737905 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.932737905 + -0.5 x = -0.932737905 + -0.5 Combine like terms: -0.932737905 + -0.5 = -1.432737905 x = -1.432737905 Simplifying x = -1.432737905Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.432737905, -1.432737905}
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