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Simplifying 6x = 4x2 + -12x + 5 Reorder the terms: 6x = 5 + -12x + 4x2 Solving 6x = 5 + -12x + 4x2 Solving for variable 'x'. Reorder the terms: -5 + 6x + 12x + -4x2 = 5 + -12x + 4x2 + -5 + 12x + -4x2 Combine like terms: 6x + 12x = 18x -5 + 18x + -4x2 = 5 + -12x + 4x2 + -5 + 12x + -4x2 Reorder the terms: -5 + 18x + -4x2 = 5 + -5 + -12x + 12x + 4x2 + -4x2 Combine like terms: 5 + -5 = 0 -5 + 18x + -4x2 = 0 + -12x + 12x + 4x2 + -4x2 -5 + 18x + -4x2 = -12x + 12x + 4x2 + -4x2 Combine like terms: -12x + 12x = 0 -5 + 18x + -4x2 = 0 + 4x2 + -4x2 -5 + 18x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + 18x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.25 + -4.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -4.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -4.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -4.5x + x2 = 0 + -1.25 -4.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -4.5x + x2 = -1.25 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -1.25 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -1.25 + 5.0625 Combine like terms: -1.25 + 5.0625 = 3.8125 5.0625 + -4.5x + x2 = 3.8125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (x + -2.25) equal to 1.952562419 and -1.952562419.Subproblem 1
x + -2.25 = 1.952562419 Simplifying x + -2.25 = 1.952562419 Reorder the terms: -2.25 + x = 1.952562419 Solving -2.25 + x = 1.952562419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.952562419 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.952562419 + 2.25 x = 1.952562419 + 2.25 Combine like terms: 1.952562419 + 2.25 = 4.202562419 x = 4.202562419 Simplifying x = 4.202562419Subproblem 2
x + -2.25 = -1.952562419 Simplifying x + -2.25 = -1.952562419 Reorder the terms: -2.25 + x = -1.952562419 Solving -2.25 + x = -1.952562419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.952562419 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.952562419 + 2.25 x = -1.952562419 + 2.25 Combine like terms: -1.952562419 + 2.25 = 0.297437581 x = 0.297437581 Simplifying x = 0.297437581Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.202562419, 0.297437581}
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