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Simplifying 3x + -5x(x + -6) = 2(x + -10) + 10 Reorder the terms: 3x + -5x(-6 + x) = 2(x + -10) + 10 3x + (-6 * -5x + x * -5x) = 2(x + -10) + 10 3x + (30x + -5x2) = 2(x + -10) + 10 Combine like terms: 3x + 30x = 33x 33x + -5x2 = 2(x + -10) + 10 Reorder the terms: 33x + -5x2 = 2(-10 + x) + 10 33x + -5x2 = (-10 * 2 + x * 2) + 10 33x + -5x2 = (-20 + 2x) + 10 Reorder the terms: 33x + -5x2 = -20 + 10 + 2x Combine like terms: -20 + 10 = -10 33x + -5x2 = -10 + 2x Solving 33x + -5x2 = -10 + 2x Solving for variable 'x'. Reorder the terms: 10 + 33x + -2x + -5x2 = -10 + 2x + 10 + -2x Combine like terms: 33x + -2x = 31x 10 + 31x + -5x2 = -10 + 2x + 10 + -2x Reorder the terms: 10 + 31x + -5x2 = -10 + 10 + 2x + -2x Combine like terms: -10 + 10 = 0 10 + 31x + -5x2 = 0 + 2x + -2x 10 + 31x + -5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 10 + 31x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2 + -6.2x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -6.2x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -6.2x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6.2x + x2 = 0 + 2 -6.2x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6.2x + x2 = 2 The x term is -6.2x. Take half its coefficient (-3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. -6.2x + 9.61 + x2 = 2 + 9.61 Reorder the terms: 9.61 + -6.2x + x2 = 2 + 9.61 Combine like terms: 2 + 9.61 = 11.61 9.61 + -6.2x + x2 = 11.61 Factor a perfect square on the left side: (x + -3.1)(x + -3.1) = 11.61 Calculate the square root of the right side: 3.407345007 Break this problem into two subproblems by setting (x + -3.1) equal to 3.407345007 and -3.407345007.Subproblem 1
x + -3.1 = 3.407345007 Simplifying x + -3.1 = 3.407345007 Reorder the terms: -3.1 + x = 3.407345007 Solving -3.1 + x = 3.407345007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.1' to each side of the equation. -3.1 + 3.1 + x = 3.407345007 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + x = 3.407345007 + 3.1 x = 3.407345007 + 3.1 Combine like terms: 3.407345007 + 3.1 = 6.507345007 x = 6.507345007 Simplifying x = 6.507345007Subproblem 2
x + -3.1 = -3.407345007 Simplifying x + -3.1 = -3.407345007 Reorder the terms: -3.1 + x = -3.407345007 Solving -3.1 + x = -3.407345007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.1' to each side of the equation. -3.1 + 3.1 + x = -3.407345007 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + x = -3.407345007 + 3.1 x = -3.407345007 + 3.1 Combine like terms: -3.407345007 + 3.1 = -0.307345007 x = -0.307345007 Simplifying x = -0.307345007Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.507345007, -0.307345007}
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