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Simplifying x(2x + -2) = 35 Reorder the terms: x(-2 + 2x) = 35 (-2 * x + 2x * x) = 35 (-2x + 2x2) = 35 Solving -2x + 2x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + -2x + 2x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -1x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -1x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -1x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -1x + x2 = 0 + 17.5 -1x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -1x + x2 = 17.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 17.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 17.5 + 0.25 Combine like terms: 17.5 + 0.25 = 17.75 0.25 + -1x + x2 = 17.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (x + -0.5) equal to 4.213074887 and -4.213074887.Subproblem 1
x + -0.5 = 4.213074887 Simplifying x + -0.5 = 4.213074887 Reorder the terms: -0.5 + x = 4.213074887 Solving -0.5 + x = 4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.213074887 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.213074887 + 0.5 x = 4.213074887 + 0.5 Combine like terms: 4.213074887 + 0.5 = 4.713074887 x = 4.713074887 Simplifying x = 4.713074887Subproblem 2
x + -0.5 = -4.213074887 Simplifying x + -0.5 = -4.213074887 Reorder the terms: -0.5 + x = -4.213074887 Solving -0.5 + x = -4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.213074887 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.213074887 + 0.5 x = -4.213074887 + 0.5 Combine like terms: -4.213074887 + 0.5 = -3.713074887 x = -3.713074887 Simplifying x = -3.713074887Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.713074887, -3.713074887}
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