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Simplifying 3x(2 + -1x) + -5x(7 + -2x) = 10 + -4x + 5 (2 * 3x + -1x * 3x) + -5x(7 + -2x) = 10 + -4x + 5 (6x + -3x2) + -5x(7 + -2x) = 10 + -4x + 5 6x + -3x2 + (7 * -5x + -2x * -5x) = 10 + -4x + 5 6x + -3x2 + (-35x + 10x2) = 10 + -4x + 5 Reorder the terms: 6x + -35x + -3x2 + 10x2 = 10 + -4x + 5 Combine like terms: 6x + -35x = -29x -29x + -3x2 + 10x2 = 10 + -4x + 5 Combine like terms: -3x2 + 10x2 = 7x2 -29x + 7x2 = 10 + -4x + 5 Reorder the terms: -29x + 7x2 = 10 + 5 + -4x Combine like terms: 10 + 5 = 15 -29x + 7x2 = 15 + -4x Solving -29x + 7x2 = 15 + -4x Solving for variable 'x'. Reorder the terms: -15 + -29x + 4x + 7x2 = 15 + -4x + -15 + 4x Combine like terms: -29x + 4x = -25x -15 + -25x + 7x2 = 15 + -4x + -15 + 4x Reorder the terms: -15 + -25x + 7x2 = 15 + -15 + -4x + 4x Combine like terms: 15 + -15 = 0 -15 + -25x + 7x2 = 0 + -4x + 4x -15 + -25x + 7x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -15 + -25x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.142857143 + -3.571428571x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + -3.571428571x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + -3.571428571x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + -3.571428571x + x2 = 0 + 2.142857143 -3.571428571x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 -3.571428571x + x2 = 2.142857143 The x term is -3.571428571x. Take half its coefficient (-1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. -3.571428571x + 3.188775511 + x2 = 2.142857143 + 3.188775511 Reorder the terms: 3.188775511 + -3.571428571x + x2 = 2.142857143 + 3.188775511 Combine like terms: 2.142857143 + 3.188775511 = 5.331632654 3.188775511 + -3.571428571x + x2 = 5.331632654 Factor a perfect square on the left side: (x + -1.785714286)(x + -1.785714286) = 5.331632654 Calculate the square root of the right side: 2.30903284 Break this problem into two subproblems by setting (x + -1.785714286) equal to 2.30903284 and -2.30903284.Subproblem 1
x + -1.785714286 = 2.30903284 Simplifying x + -1.785714286 = 2.30903284 Reorder the terms: -1.785714286 + x = 2.30903284 Solving -1.785714286 + x = 2.30903284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = 2.30903284 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = 2.30903284 + 1.785714286 x = 2.30903284 + 1.785714286 Combine like terms: 2.30903284 + 1.785714286 = 4.094747126 x = 4.094747126 Simplifying x = 4.094747126Subproblem 2
x + -1.785714286 = -2.30903284 Simplifying x + -1.785714286 = -2.30903284 Reorder the terms: -1.785714286 + x = -2.30903284 Solving -1.785714286 + x = -2.30903284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = -2.30903284 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = -2.30903284 + 1.785714286 x = -2.30903284 + 1.785714286 Combine like terms: -2.30903284 + 1.785714286 = -0.523318554 x = -0.523318554 Simplifying x = -0.523318554Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.094747126, -0.523318554}
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