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Simplifying (x)(2x + -7) = 530 Reorder the terms: x(-7 + 2x) = 530 (-7 * x + 2x * x) = 530 (-7x + 2x2) = 530 Solving -7x + 2x2 = 530 Solving for variable 'x'. Reorder the terms: -530 + -7x + 2x2 = 530 + -530 Combine like terms: 530 + -530 = 0 -530 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -265 + -3.5x + x2 = 0 Move the constant term to the right: Add '265' to each side of the equation. -265 + -3.5x + 265 + x2 = 0 + 265 Reorder the terms: -265 + 265 + -3.5x + x2 = 0 + 265 Combine like terms: -265 + 265 = 0 0 + -3.5x + x2 = 0 + 265 -3.5x + x2 = 0 + 265 Combine like terms: 0 + 265 = 265 -3.5x + x2 = 265 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 = 265 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 265 + 3.0625 Combine like terms: 265 + 3.0625 = 268.0625 3.0625 + -3.5x + x2 = 268.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 268.0625 Calculate the square root of the right side: 16.37261433 Break this problem into two subproblems by setting (x + -1.75) equal to 16.37261433 and -16.37261433.Subproblem 1
x + -1.75 = 16.37261433 Simplifying x + -1.75 = 16.37261433 Reorder the terms: -1.75 + x = 16.37261433 Solving -1.75 + x = 16.37261433 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 = 16.37261433 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 16.37261433 + 1.75 x = 16.37261433 + 1.75 Combine like terms: 16.37261433 + 1.75 = 18.12261433 x = 18.12261433 Simplifying x = 18.12261433Subproblem 2
x + -1.75 = -16.37261433 Simplifying x + -1.75 = -16.37261433 Reorder the terms: -1.75 + x = -16.37261433 Solving -1.75 + x = -16.37261433 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 = -16.37261433 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -16.37261433 + 1.75 x = -16.37261433 + 1.75 Combine like terms: -16.37261433 + 1.75 = -14.62261433 x = -14.62261433 Simplifying x = -14.62261433Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.12261433, -14.62261433}
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