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Simplifying 2x(x + -7) + 2x = 6x + 15 Reorder the terms: 2x(-7 + x) + 2x = 6x + 15 (-7 * 2x + x * 2x) + 2x = 6x + 15 (-14x + 2x2) + 2x = 6x + 15 Reorder the terms: -14x + 2x + 2x2 = 6x + 15 Combine like terms: -14x + 2x = -12x -12x + 2x2 = 6x + 15 Reorder the terms: -12x + 2x2 = 15 + 6x Solving -12x + 2x2 = 15 + 6x Solving for variable 'x'. Reorder the terms: -15 + -12x + -6x + 2x2 = 15 + 6x + -15 + -6x Combine like terms: -12x + -6x = -18x -15 + -18x + 2x2 = 15 + 6x + -15 + -6x Reorder the terms: -15 + -18x + 2x2 = 15 + -15 + 6x + -6x Combine like terms: 15 + -15 = 0 -15 + -18x + 2x2 = 0 + 6x + -6x -15 + -18x + 2x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -15 + -18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -9x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -9x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -9x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -9x + x2 = 0 + 7.5 -9x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -9x + x2 = 7.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 7.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 7.5 + 20.25 Combine like terms: 7.5 + 20.25 = 27.75 20.25 + -9x + x2 = 27.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 27.75 Calculate the square root of the right side: 5.267826876 Break this problem into two subproblems by setting (x + -4.5) equal to 5.267826876 and -5.267826876.Subproblem 1
x + -4.5 = 5.267826876 Simplifying x + -4.5 = 5.267826876 Reorder the terms: -4.5 + x = 5.267826876 Solving -4.5 + x = 5.267826876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.267826876 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.267826876 + 4.5 x = 5.267826876 + 4.5 Combine like terms: 5.267826876 + 4.5 = 9.767826876 x = 9.767826876 Simplifying x = 9.767826876Subproblem 2
x + -4.5 = -5.267826876 Simplifying x + -4.5 = -5.267826876 Reorder the terms: -4.5 + x = -5.267826876 Solving -4.5 + x = -5.267826876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.267826876 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.267826876 + 4.5 x = -5.267826876 + 4.5 Combine like terms: -5.267826876 + 4.5 = -0.767826876 x = -0.767826876 Simplifying x = -0.767826876Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.767826876, -0.767826876}
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