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Simplifying 10x2 + -76x + 33 = 0 Reorder the terms: 33 + -76x + 10x2 = 0 Solving 33 + -76x + 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'. 3.3 + -7.6x + x2 = 0 Move the constant term to the right: Add '-3.3' to each side of the equation. 3.3 + -7.6x + -3.3 + x2 = 0 + -3.3 Reorder the terms: 3.3 + -3.3 + -7.6x + x2 = 0 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + -7.6x + x2 = 0 + -3.3 -7.6x + x2 = 0 + -3.3 Combine like terms: 0 + -3.3 = -3.3 -7.6x + x2 = -3.3 The x term is -7.6x. Take half its coefficient (-3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. -7.6x + 14.44 + x2 = -3.3 + 14.44 Reorder the terms: 14.44 + -7.6x + x2 = -3.3 + 14.44 Combine like terms: -3.3 + 14.44 = 11.14 14.44 + -7.6x + x2 = 11.14 Factor a perfect square on the left side: (x + -3.8)(x + -3.8) = 11.14 Calculate the square root of the right side: 3.337663854 Break this problem into two subproblems by setting (x + -3.8) equal to 3.337663854 and -3.337663854.Subproblem 1
x + -3.8 = 3.337663854 Simplifying x + -3.8 = 3.337663854 Reorder the terms: -3.8 + x = 3.337663854 Solving -3.8 + x = 3.337663854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = 3.337663854 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = 3.337663854 + 3.8 x = 3.337663854 + 3.8 Combine like terms: 3.337663854 + 3.8 = 7.137663854 x = 7.137663854 Simplifying x = 7.137663854Subproblem 2
x + -3.8 = -3.337663854 Simplifying x + -3.8 = -3.337663854 Reorder the terms: -3.8 + x = -3.337663854 Solving -3.8 + x = -3.337663854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = -3.337663854 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = -3.337663854 + 3.8 x = -3.337663854 + 3.8 Combine like terms: -3.337663854 + 3.8 = 0.462336146 x = 0.462336146 Simplifying x = 0.462336146Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.137663854, 0.462336146}
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