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Simplifying x(2x + -7) = 7 Reorder the terms: x(-7 + 2x) = 7 (-7 * x + 2x * x) = 7 (-7x + 2x2) = 7 Solving -7x + 2x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -7x + 2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -3.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -3.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -3.5x + x2 = 0 + 3.5 -3.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -3.5x + x2 = 3.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 3.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 3.5 + 3.0625 Combine like terms: 3.5 + 3.0625 = 6.5625 3.0625 + -3.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + -1.75) equal to 2.561737691 and -2.561737691.Subproblem 1
x + -1.75 = 2.561737691 Simplifying x + -1.75 = 2.561737691 Reorder the terms: -1.75 + x = 2.561737691 Solving -1.75 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.561737691 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.561737691 + 1.75 x = 2.561737691 + 1.75 Combine like terms: 2.561737691 + 1.75 = 4.311737691 x = 4.311737691 Simplifying x = 4.311737691Subproblem 2
x + -1.75 = -2.561737691 Simplifying x + -1.75 = -2.561737691 Reorder the terms: -1.75 + x = -2.561737691 Solving -1.75 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.561737691 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.561737691 + 1.75 x = -2.561737691 + 1.75 Combine like terms: -2.561737691 + 1.75 = -0.811737691 x = -0.811737691 Simplifying x = -0.811737691Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.311737691, -0.811737691}
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