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Simplifying (x + -10)(x + -10) = 12 Reorder the terms: (-10 + x)(x + -10) = 12 Reorder the terms: (-10 + x)(-10 + x) = 12 Multiply (-10 + x) * (-10 + x) (-10(-10 + x) + x(-10 + x)) = 12 ((-10 * -10 + x * -10) + x(-10 + x)) = 12 ((100 + -10x) + x(-10 + x)) = 12 (100 + -10x + (-10 * x + x * x)) = 12 (100 + -10x + (-10x + x2)) = 12 Combine like terms: -10x + -10x = -20x (100 + -20x + x2) = 12 Solving 100 + -20x + x2 = 12 Solving for variable 'x'. Reorder the terms: 100 + -12 + -20x + x2 = 12 + -12 Combine like terms: 100 + -12 = 88 88 + -20x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 88 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-88' to each side of the equation. 88 + -20x + -88 + x2 = 0 + -88 Reorder the terms: 88 + -88 + -20x + x2 = 0 + -88 Combine like terms: 88 + -88 = 0 0 + -20x + x2 = 0 + -88 -20x + x2 = 0 + -88 Combine like terms: 0 + -88 = -88 -20x + x2 = -88 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -88 + 100 Reorder the terms: 100 + -20x + x2 = -88 + 100 Combine like terms: -88 + 100 = 12 100 + -20x + x2 = 12 Factor a perfect square on the left side: (x + -10)(x + -10) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -10) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -10 = 3.464101615 Simplifying x + -10 = 3.464101615 Reorder the terms: -10 + x = 3.464101615 Solving -10 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 3.464101615 + 10 Combine like terms: -10 + 10 = 0 0 + x = 3.464101615 + 10 x = 3.464101615 + 10 Combine like terms: 3.464101615 + 10 = 13.464101615 x = 13.464101615 Simplifying x = 13.464101615Subproblem 2
x + -10 = -3.464101615 Simplifying x + -10 = -3.464101615 Reorder the terms: -10 + x = -3.464101615 Solving -10 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -3.464101615 + 10 Combine like terms: -10 + 10 = 0 0 + x = -3.464101615 + 10 x = -3.464101615 + 10 Combine like terms: -3.464101615 + 10 = 6.535898385 x = 6.535898385 Simplifying x = 6.535898385Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.464101615, 6.535898385}
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