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Simplifying 2x(x + -8) + 10x = 7x + 39 Reorder the terms: 2x(-8 + x) + 10x = 7x + 39 (-8 * 2x + x * 2x) + 10x = 7x + 39 (-16x + 2x2) + 10x = 7x + 39 Reorder the terms: -16x + 10x + 2x2 = 7x + 39 Combine like terms: -16x + 10x = -6x -6x + 2x2 = 7x + 39 Reorder the terms: -6x + 2x2 = 39 + 7x Solving -6x + 2x2 = 39 + 7x Solving for variable 'x'. Reorder the terms: -39 + -6x + -7x + 2x2 = 39 + 7x + -39 + -7x Combine like terms: -6x + -7x = -13x -39 + -13x + 2x2 = 39 + 7x + -39 + -7x Reorder the terms: -39 + -13x + 2x2 = 39 + -39 + 7x + -7x Combine like terms: 39 + -39 = 0 -39 + -13x + 2x2 = 0 + 7x + -7x -39 + -13x + 2x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -39 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + -6.5x + 19.5 + x2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + -6.5x + x2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + -6.5x + x2 = 0 + 19.5 -6.5x + x2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 -6.5x + x2 = 19.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 19.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 19.5 + 10.5625 Combine like terms: 19.5 + 10.5625 = 30.0625 10.5625 + -6.5x + x2 = 30.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 30.0625 Calculate the square root of the right side: 5.48292805 Break this problem into two subproblems by setting (x + -3.25) equal to 5.48292805 and -5.48292805.Subproblem 1
x + -3.25 = 5.48292805 Simplifying x + -3.25 = 5.48292805 Reorder the terms: -3.25 + x = 5.48292805 Solving -3.25 + x = 5.48292805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 5.48292805 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 5.48292805 + 3.25 x = 5.48292805 + 3.25 Combine like terms: 5.48292805 + 3.25 = 8.73292805 x = 8.73292805 Simplifying x = 8.73292805Subproblem 2
x + -3.25 = -5.48292805 Simplifying x + -3.25 = -5.48292805 Reorder the terms: -3.25 + x = -5.48292805 Solving -3.25 + x = -5.48292805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -5.48292805 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -5.48292805 + 3.25 x = -5.48292805 + 3.25 Combine like terms: -5.48292805 + 3.25 = -2.23292805 x = -2.23292805 Simplifying x = -2.23292805Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.73292805, -2.23292805}
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