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Simplifying 5x2 = 12x + 31 Reorder the terms: 5x2 = 31 + 12x Solving 5x2 = 31 + 12x Solving for variable 'x'. Reorder the terms: -31 + -12x + 5x2 = 31 + 12x + -31 + -12x Reorder the terms: -31 + -12x + 5x2 = 31 + -31 + 12x + -12x Combine like terms: 31 + -31 = 0 -31 + -12x + 5x2 = 0 + 12x + -12x -31 + -12x + 5x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -31 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.2 + -2.4x + x2 = 0 Move the constant term to the right: Add '6.2' to each side of the equation. -6.2 + -2.4x + 6.2 + x2 = 0 + 6.2 Reorder the terms: -6.2 + 6.2 + -2.4x + x2 = 0 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + -2.4x + x2 = 0 + 6.2 -2.4x + x2 = 0 + 6.2 Combine like terms: 0 + 6.2 = 6.2 -2.4x + x2 = 6.2 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 = 6.2 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 6.2 + 1.44 Combine like terms: 6.2 + 1.44 = 7.64 1.44 + -2.4x + x2 = 7.64 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 7.64 Calculate the square root of the right side: 2.764054992 Break this problem into two subproblems by setting (x + -1.2) equal to 2.764054992 and -2.764054992.Subproblem 1
x + -1.2 = 2.764054992 Simplifying x + -1.2 = 2.764054992 Reorder the terms: -1.2 + x = 2.764054992 Solving -1.2 + x = 2.764054992 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 = 2.764054992 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 2.764054992 + 1.2 x = 2.764054992 + 1.2 Combine like terms: 2.764054992 + 1.2 = 3.964054992 x = 3.964054992 Simplifying x = 3.964054992Subproblem 2
x + -1.2 = -2.764054992 Simplifying x + -1.2 = -2.764054992 Reorder the terms: -1.2 + x = -2.764054992 Solving -1.2 + x = -2.764054992 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 = -2.764054992 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -2.764054992 + 1.2 x = -2.764054992 + 1.2 Combine like terms: -2.764054992 + 1.2 = -1.564054992 x = -1.564054992 Simplifying x = -1.564054992Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.964054992, -1.564054992}
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