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Simplifying 2x(x + -7) = 5 Reorder the terms: 2x(-7 + x) = 5 (-7 * 2x + x * 2x) = 5 (-14x + 2x2) = 5 Solving -14x + 2x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -14x + 2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -7x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -7x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -7x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -7x + x2 = 0 + 2.5 -7x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -7x + x2 = 2.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 2.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 2.5 + 12.25 Combine like terms: 2.5 + 12.25 = 14.75 12.25 + -7x + x2 = 14.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 14.75 Calculate the square root of the right side: 3.840572874 Break this problem into two subproblems by setting (x + -3.5) equal to 3.840572874 and -3.840572874.Subproblem 1
x + -3.5 = 3.840572874 Simplifying x + -3.5 = 3.840572874 Reorder the terms: -3.5 + x = 3.840572874 Solving -3.5 + x = 3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.840572874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.840572874 + 3.5 x = 3.840572874 + 3.5 Combine like terms: 3.840572874 + 3.5 = 7.340572874 x = 7.340572874 Simplifying x = 7.340572874Subproblem 2
x + -3.5 = -3.840572874 Simplifying x + -3.5 = -3.840572874 Reorder the terms: -3.5 + x = -3.840572874 Solving -3.5 + x = -3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.840572874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.840572874 + 3.5 x = -3.840572874 + 3.5 Combine like terms: -3.840572874 + 3.5 = -0.340572874 x = -0.340572874 Simplifying x = -0.340572874Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.340572874, -0.340572874}
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