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Simplifying 0 = -13 + 24x + -10x2 Solving 0 = -13 + 24x + -10x2 Solving for variable 'x'. Combine like terms: 0 + 13 = 13 13 + -24x + 10x2 = -13 + 24x + -10x2 + 13 + -24x + 10x2 Reorder the terms: 13 + -24x + 10x2 = -13 + 13 + 24x + -24x + -10x2 + 10x2 Combine like terms: -13 + 13 = 0 13 + -24x + 10x2 = 0 + 24x + -24x + -10x2 + 10x2 13 + -24x + 10x2 = 24x + -24x + -10x2 + 10x2 Combine like terms: 24x + -24x = 0 13 + -24x + 10x2 = 0 + -10x2 + 10x2 13 + -24x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 13 + -24x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.3 + -2.4x + x2 = 0 Move the constant term to the right: Add '-1.3' to each side of the equation. 1.3 + -2.4x + -1.3 + x2 = 0 + -1.3 Reorder the terms: 1.3 + -1.3 + -2.4x + x2 = 0 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + -2.4x + x2 = 0 + -1.3 -2.4x + x2 = 0 + -1.3 Combine like terms: 0 + -1.3 = -1.3 -2.4x + x2 = -1.3 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 = -1.3 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -1.3 + 1.44 Combine like terms: -1.3 + 1.44 = 0.14 1.44 + -2.4x + x2 = 0.14 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.14 Calculate the square root of the right side: 0.374165739 Break this problem into two subproblems by setting (x + -1.2) equal to 0.374165739 and -0.374165739.Subproblem 1
x + -1.2 = 0.374165739 Simplifying x + -1.2 = 0.374165739 Reorder the terms: -1.2 + x = 0.374165739 Solving -1.2 + x = 0.374165739 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 = 0.374165739 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.374165739 + 1.2 x = 0.374165739 + 1.2 Combine like terms: 0.374165739 + 1.2 = 1.574165739 x = 1.574165739 Simplifying x = 1.574165739Subproblem 2
x + -1.2 = -0.374165739 Simplifying x + -1.2 = -0.374165739 Reorder the terms: -1.2 + x = -0.374165739 Solving -1.2 + x = -0.374165739 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 = -0.374165739 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.374165739 + 1.2 x = -0.374165739 + 1.2 Combine like terms: -0.374165739 + 1.2 = 0.825834261 x = 0.825834261 Simplifying x = 0.825834261Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.574165739, 0.825834261}
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