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Simplifying 10x2 = 29x + -3 Reorder the terms: 10x2 = -3 + 29x Solving 10x2 = -3 + 29x Solving for variable 'x'. Reorder the terms: 3 + -29x + 10x2 = -3 + 29x + 3 + -29x Reorder the terms: 3 + -29x + 10x2 = -3 + 3 + 29x + -29x Combine like terms: -3 + 3 = 0 3 + -29x + 10x2 = 0 + 29x + -29x 3 + -29x + 10x2 = 29x + -29x Combine like terms: 29x + -29x = 0 3 + -29x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.3 + -2.9x + x2 = 0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -2.9x + -0.3 + x2 = 0 + -0.3 Reorder the terms: 0.3 + -0.3 + -2.9x + x2 = 0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -2.9x + x2 = 0 + -0.3 -2.9x + x2 = 0 + -0.3 Combine like terms: 0 + -0.3 = -0.3 -2.9x + x2 = -0.3 The x term is -2.9x. Take half its coefficient (-1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. -2.9x + 2.1025 + x2 = -0.3 + 2.1025 Reorder the terms: 2.1025 + -2.9x + x2 = -0.3 + 2.1025 Combine like terms: -0.3 + 2.1025 = 1.8025 2.1025 + -2.9x + x2 = 1.8025 Factor a perfect square on the left side: (x + -1.45)(x + -1.45) = 1.8025 Calculate the square root of the right side: 1.342572158 Break this problem into two subproblems by setting (x + -1.45) equal to 1.342572158 and -1.342572158.Subproblem 1
x + -1.45 = 1.342572158 Simplifying x + -1.45 = 1.342572158 Reorder the terms: -1.45 + x = 1.342572158 Solving -1.45 + x = 1.342572158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = 1.342572158 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = 1.342572158 + 1.45 x = 1.342572158 + 1.45 Combine like terms: 1.342572158 + 1.45 = 2.792572158 x = 2.792572158 Simplifying x = 2.792572158Subproblem 2
x + -1.45 = -1.342572158 Simplifying x + -1.45 = -1.342572158 Reorder the terms: -1.45 + x = -1.342572158 Solving -1.45 + x = -1.342572158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = -1.342572158 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = -1.342572158 + 1.45 x = -1.342572158 + 1.45 Combine like terms: -1.342572158 + 1.45 = 0.107427842 x = 0.107427842 Simplifying x = 0.107427842Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.792572158, 0.107427842}
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