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Simplifying 10x2 + -24x + 9 = 0 Reorder the terms: 9 + -24x + 10x2 = 0 Solving 9 + -24x + 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'. 0.9 + -2.4x + x2 = 0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + -2.4x + -0.9 + x2 = 0 + -0.9 Reorder the terms: 0.9 + -0.9 + -2.4x + x2 = 0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + -2.4x + x2 = 0 + -0.9 -2.4x + x2 = 0 + -0.9 Combine like terms: 0 + -0.9 = -0.9 -2.4x + x2 = -0.9 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -0.9 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -0.9 + 1.44 Combine like terms: -0.9 + 1.44 = 0.54 1.44 + -2.4x + x2 = 0.54 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.54 Calculate the square root of the right side: 0.734846923 Break this problem into two subproblems by setting (x + -1.2) equal to 0.734846923 and -0.734846923.Subproblem 1
x + -1.2 = 0.734846923 Simplifying x + -1.2 = 0.734846923 Reorder the terms: -1.2 + x = 0.734846923 Solving -1.2 + x = 0.734846923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 0.734846923 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.734846923 + 1.2 x = 0.734846923 + 1.2 Combine like terms: 0.734846923 + 1.2 = 1.934846923 x = 1.934846923 Simplifying x = 1.934846923Subproblem 2
x + -1.2 = -0.734846923 Simplifying x + -1.2 = -0.734846923 Reorder the terms: -1.2 + x = -0.734846923 Solving -1.2 + x = -0.734846923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -0.734846923 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.734846923 + 1.2 x = -0.734846923 + 1.2 Combine like terms: -0.734846923 + 1.2 = 0.465153077 x = 0.465153077 Simplifying x = 0.465153077Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.934846923, 0.465153077}
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