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Simplifying 3x2 + -20x = 4x2 + -7x + -6 Reorder the terms: -20x + 3x2 = 4x2 + -7x + -6 Reorder the terms: -20x + 3x2 = -6 + -7x + 4x2 Solving -20x + 3x2 = -6 + -7x + 4x2 Solving for variable 'x'. Reorder the terms: 6 + -20x + 7x + 3x2 + -4x2 = -6 + -7x + 4x2 + 6 + 7x + -4x2 Combine like terms: -20x + 7x = -13x 6 + -13x + 3x2 + -4x2 = -6 + -7x + 4x2 + 6 + 7x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 6 + -13x + -1x2 = -6 + -7x + 4x2 + 6 + 7x + -4x2 Reorder the terms: 6 + -13x + -1x2 = -6 + 6 + -7x + 7x + 4x2 + -4x2 Combine like terms: -6 + 6 = 0 6 + -13x + -1x2 = 0 + -7x + 7x + 4x2 + -4x2 6 + -13x + -1x2 = -7x + 7x + 4x2 + -4x2 Combine like terms: -7x + 7x = 0 6 + -13x + -1x2 = 0 + 4x2 + -4x2 6 + -13x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 6 + -13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + 13x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 13x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 13x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 13x + x2 = 0 + 6 13x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 13x + x2 = 6 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 6 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 6 + 42.25 Combine like terms: 6 + 42.25 = 48.25 42.25 + 13x + x2 = 48.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + 6.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + 6.5 = 6.946221995 Simplifying x + 6.5 = 6.946221995 Reorder the terms: 6.5 + x = 6.946221995 Solving 6.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 6.946221995 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.946221995 + -6.5 x = 6.946221995 + -6.5 Combine like terms: 6.946221995 + -6.5 = 0.446221995 x = 0.446221995 Simplifying x = 0.446221995Subproblem 2
x + 6.5 = -6.946221995 Simplifying x + 6.5 = -6.946221995 Reorder the terms: 6.5 + x = -6.946221995 Solving 6.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -6.946221995 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.946221995 + -6.5 x = -6.946221995 + -6.5 Combine like terms: -6.946221995 + -6.5 = -13.446221995 x = -13.446221995 Simplifying x = -13.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.446221995, -13.446221995}
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