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Simplifying 10x2 + x + -2 = 10 Reorder the terms: -2 + x + 10x2 = 10 Solving -2 + x + 10x2 = 10 Solving for variable 'x'. Reorder the terms: -2 + -10 + x + 10x2 = 10 + -10 Combine like terms: -2 + -10 = -12 -12 + x + 10x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -12 + x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.2 + 0.1x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.1x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.1x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.1x + x2 = 0 + 1.2 0.1x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.1x + x2 = 1.2 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 = 1.2 + 0.25 Reorder the terms: 0.25 + 0.1x + x2 = 1.2 + 0.25 Combine like terms: 1.2 + 0.25 = 1.45 0.25 + 0.1x + x2 = 1.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (x + 0.5) equal to 1.204159458 and -1.204159458.Subproblem 1
x + 0.5 = 1.204159458 Simplifying x + 0.5 = 1.204159458 Reorder the terms: 0.5 + x = 1.204159458 Solving 0.5 + x = 1.204159458 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 = 1.204159458 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.204159458 + -0.5 x = 1.204159458 + -0.5 Combine like terms: 1.204159458 + -0.5 = 0.704159458 x = 0.704159458 Simplifying x = 0.704159458Subproblem 2
x + 0.5 = -1.204159458 Simplifying x + 0.5 = -1.204159458 Reorder the terms: 0.5 + x = -1.204159458 Solving 0.5 + x = -1.204159458 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 = -1.204159458 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.204159458 + -0.5 x = -1.204159458 + -0.5 Combine like terms: -1.204159458 + -0.5 = -1.704159458 x = -1.704159458 Simplifying x = -1.704159458Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.704159458, -1.704159458}
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