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Simplifying 2x + 5(3x + -4)(x) = 3520 Reorder the terms: 2x + 5(-4 + 3x)(x) = 3520 Reorder the terms for easier multiplication: 2x + 5x(-4 + 3x) = 3520 2x + (-4 * 5x + 3x * 5x) = 3520 2x + (-20x + 15x2) = 3520 Combine like terms: 2x + -20x = -18x -18x + 15x2 = 3520 Solving -18x + 15x2 = 3520 Solving for variable 'x'. Reorder the terms: -3520 + -18x + 15x2 = 3520 + -3520 Combine like terms: 3520 + -3520 = 0 -3520 + -18x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -234.6666667 + -1.2x + x2 = 0 Move the constant term to the right: Add '234.6666667' to each side of the equation. -234.6666667 + -1.2x + 234.6666667 + x2 = 0 + 234.6666667 Reorder the terms: -234.6666667 + 234.6666667 + -1.2x + x2 = 0 + 234.6666667 Combine like terms: -234.6666667 + 234.6666667 = 0.0000000 0.0000000 + -1.2x + x2 = 0 + 234.6666667 -1.2x + x2 = 0 + 234.6666667 Combine like terms: 0 + 234.6666667 = 234.6666667 -1.2x + x2 = 234.6666667 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 234.6666667 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 234.6666667 + 0.36 Combine like terms: 234.6666667 + 0.36 = 235.0266667 0.36 + -1.2x + x2 = 235.0266667 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 235.0266667 Calculate the square root of the right side: 15.330579464 Break this problem into two subproblems by setting (x + -0.6) equal to 15.330579464 and -15.330579464.Subproblem 1
x + -0.6 = 15.330579464 Simplifying x + -0.6 = 15.330579464 Reorder the terms: -0.6 + x = 15.330579464 Solving -0.6 + x = 15.330579464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 15.330579464 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 15.330579464 + 0.6 x = 15.330579464 + 0.6 Combine like terms: 15.330579464 + 0.6 = 15.930579464 x = 15.930579464 Simplifying x = 15.930579464Subproblem 2
x + -0.6 = -15.330579464 Simplifying x + -0.6 = -15.330579464 Reorder the terms: -0.6 + x = -15.330579464 Solving -0.6 + x = -15.330579464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -15.330579464 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -15.330579464 + 0.6 x = -15.330579464 + 0.6 Combine like terms: -15.330579464 + 0.6 = -14.730579464 x = -14.730579464 Simplifying x = -14.730579464Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.930579464, -14.730579464}
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