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Simplifying -3x + 6x + -5x(x + -1) = -5x + -1(2x + -4) + 5 Reorder the terms: -3x + 6x + -5x(-1 + x) = -5x + -1(2x + -4) + 5 -3x + 6x + (-1 * -5x + x * -5x) = -5x + -1(2x + -4) + 5 -3x + 6x + (5x + -5x2) = -5x + -1(2x + -4) + 5 Combine like terms: -3x + 6x = 3x 3x + 5x + -5x2 = -5x + -1(2x + -4) + 5 Combine like terms: 3x + 5x = 8x 8x + -5x2 = -5x + -1(2x + -4) + 5 Reorder the terms: 8x + -5x2 = -5x + -1(-4 + 2x) + 5 8x + -5x2 = -5x + (-4 * -1 + 2x * -1) + 5 8x + -5x2 = -5x + (4 + -2x) + 5 Reorder the terms: 8x + -5x2 = 4 + 5 + -5x + -2x Combine like terms: 4 + 5 = 9 8x + -5x2 = 9 + -5x + -2x Combine like terms: -5x + -2x = -7x 8x + -5x2 = 9 + -7x Solving 8x + -5x2 = 9 + -7x Solving for variable 'x'. Reorder the terms: -9 + 8x + 7x + -5x2 = 9 + -7x + -9 + 7x Combine like terms: 8x + 7x = 15x -9 + 15x + -5x2 = 9 + -7x + -9 + 7x Reorder the terms: -9 + 15x + -5x2 = 9 + -9 + -7x + 7x Combine like terms: 9 + -9 = 0 -9 + 15x + -5x2 = 0 + -7x + 7x -9 + 15x + -5x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -9 + 15x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.8 + -3x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -3x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -3x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -3x + x2 = 0 + -1.8 -3x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -3x + x2 = -1.8 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.8 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.8 + 2.25 Combine like terms: -1.8 + 2.25 = 0.45 2.25 + -3x + x2 = 0.45 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (x + -1.5) equal to 0.670820393 and -0.670820393.Subproblem 1
x + -1.5 = 0.670820393 Simplifying x + -1.5 = 0.670820393 Reorder the terms: -1.5 + x = 0.670820393 Solving -1.5 + x = 0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.670820393 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.670820393 + 1.5 x = 0.670820393 + 1.5 Combine like terms: 0.670820393 + 1.5 = 2.170820393 x = 2.170820393 Simplifying x = 2.170820393Subproblem 2
x + -1.5 = -0.670820393 Simplifying x + -1.5 = -0.670820393 Reorder the terms: -1.5 + x = -0.670820393 Solving -1.5 + x = -0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.670820393 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.670820393 + 1.5 x = -0.670820393 + 1.5 Combine like terms: -0.670820393 + 1.5 = 0.829179607 x = 0.829179607 Simplifying x = 0.829179607Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.170820393, 0.829179607}
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