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Simplifying 2x(x + -7) = 2x + -13 Reorder the terms: 2x(-7 + x) = 2x + -13 (-7 * 2x + x * 2x) = 2x + -13 (-14x + 2x2) = 2x + -13 Reorder the terms: -14x + 2x2 = -13 + 2x Solving -14x + 2x2 = -13 + 2x Solving for variable 'x'. Reorder the terms: 13 + -14x + -2x + 2x2 = -13 + 2x + 13 + -2x Combine like terms: -14x + -2x = -16x 13 + -16x + 2x2 = -13 + 2x + 13 + -2x Reorder the terms: 13 + -16x + 2x2 = -13 + 13 + 2x + -2x Combine like terms: -13 + 13 = 0 13 + -16x + 2x2 = 0 + 2x + -2x 13 + -16x + 2x2 = 2x + -2x Combine like terms: 2x + -2x = 0 13 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -8x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -8x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -8x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -8x + x2 = 0 + -6.5 -8x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -8x + x2 = -6.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -6.5 + 16 Reorder the terms: 16 + -8x + x2 = -6.5 + 16 Combine like terms: -6.5 + 16 = 9.5 16 + -8x + x2 = 9.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + -4) equal to 3.082207001 and -3.082207001.Subproblem 1
x + -4 = 3.082207001 Simplifying x + -4 = 3.082207001 Reorder the terms: -4 + x = 3.082207001 Solving -4 + x = 3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.082207001 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.082207001 + 4 x = 3.082207001 + 4 Combine like terms: 3.082207001 + 4 = 7.082207001 x = 7.082207001 Simplifying x = 7.082207001Subproblem 2
x + -4 = -3.082207001 Simplifying x + -4 = -3.082207001 Reorder the terms: -4 + x = -3.082207001 Solving -4 + x = -3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.082207001 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.082207001 + 4 x = -3.082207001 + 4 Combine like terms: -3.082207001 + 4 = 0.917792999 x = 0.917792999 Simplifying x = 0.917792999Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.082207001, 0.917792999}
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