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Simplifying 2x2 + -24x + -5 = 2 Reorder the terms: -5 + -24x + 2x2 = 2 Solving -5 + -24x + 2x2 = 2 Solving for variable 'x'. Reorder the terms: -5 + -2 + -24x + 2x2 = 2 + -2 Combine like terms: -5 + -2 = -7 -7 + -24x + 2x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -7 + -24x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -12x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -12x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -12x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -12x + x2 = 0 + 3.5 -12x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -12x + x2 = 3.5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 3.5 + 36 Reorder the terms: 36 + -12x + x2 = 3.5 + 36 Combine like terms: 3.5 + 36 = 39.5 36 + -12x + x2 = 39.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 39.5 Calculate the square root of the right side: 6.284902545 Break this problem into two subproblems by setting (x + -6) equal to 6.284902545 and -6.284902545.Subproblem 1
x + -6 = 6.284902545 Simplifying x + -6 = 6.284902545 Reorder the terms: -6 + x = 6.284902545 Solving -6 + x = 6.284902545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.284902545 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.284902545 + 6 x = 6.284902545 + 6 Combine like terms: 6.284902545 + 6 = 12.284902545 x = 12.284902545 Simplifying x = 12.284902545Subproblem 2
x + -6 = -6.284902545 Simplifying x + -6 = -6.284902545 Reorder the terms: -6 + x = -6.284902545 Solving -6 + x = -6.284902545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.284902545 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.284902545 + 6 x = -6.284902545 + 6 Combine like terms: -6.284902545 + 6 = -0.284902545 x = -0.284902545 Simplifying x = -0.284902545Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.284902545, -0.284902545}
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