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Simplifying 12.4x + -1x2 + -36 = 0 Reorder the terms: -36 + 12.4x + -1x2 = 0 Solving -36 + 12.4x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 36 + -12.4x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -12.4x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -12.4x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -12.4x + x2 = 0 + -36 -12.4x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -12.4x + x2 = -36 The x term is -12.4x. Take half its coefficient (-6.2). Square it (38.44) and add it to both sides. Add '38.44' to each side of the equation. -12.4x + 38.44 + x2 = -36 + 38.44 Reorder the terms: 38.44 + -12.4x + x2 = -36 + 38.44 Combine like terms: -36 + 38.44 = 2.44 38.44 + -12.4x + x2 = 2.44 Factor a perfect square on the left side: (x + -6.2)(x + -6.2) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (x + -6.2) equal to 1.562049935 and -1.562049935.Subproblem 1
x + -6.2 = 1.562049935 Simplifying x + -6.2 = 1.562049935 Reorder the terms: -6.2 + x = 1.562049935 Solving -6.2 + x = 1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.2' to each side of the equation. -6.2 + 6.2 + x = 1.562049935 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + x = 1.562049935 + 6.2 x = 1.562049935 + 6.2 Combine like terms: 1.562049935 + 6.2 = 7.762049935 x = 7.762049935 Simplifying x = 7.762049935Subproblem 2
x + -6.2 = -1.562049935 Simplifying x + -6.2 = -1.562049935 Reorder the terms: -6.2 + x = -1.562049935 Solving -6.2 + x = -1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.2' to each side of the equation. -6.2 + 6.2 + x = -1.562049935 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + x = -1.562049935 + 6.2 x = -1.562049935 + 6.2 Combine like terms: -1.562049935 + 6.2 = 4.637950065 x = 4.637950065 Simplifying x = 4.637950065Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.762049935, 4.637950065}
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