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Simplifying -3x + 6 + -5x(x + -1) = -5x + -1(2x + -4) + 5 Reorder the terms: -3x + 6 + -5x(-1 + x) = -5x + -1(2x + -4) + 5 -3x + 6 + (-1 * -5x + x * -5x) = -5x + -1(2x + -4) + 5 -3x + 6 + (5x + -5x2) = -5x + -1(2x + -4) + 5 Reorder the terms: 6 + -3x + 5x + -5x2 = -5x + -1(2x + -4) + 5 Combine like terms: -3x + 5x = 2x 6 + 2x + -5x2 = -5x + -1(2x + -4) + 5 Reorder the terms: 6 + 2x + -5x2 = -5x + -1(-4 + 2x) + 5 6 + 2x + -5x2 = -5x + (-4 * -1 + 2x * -1) + 5 6 + 2x + -5x2 = -5x + (4 + -2x) + 5 Reorder the terms: 6 + 2x + -5x2 = 4 + 5 + -5x + -2x Combine like terms: 4 + 5 = 9 6 + 2x + -5x2 = 9 + -5x + -2x Combine like terms: -5x + -2x = -7x 6 + 2x + -5x2 = 9 + -7x Solving 6 + 2x + -5x2 = 9 + -7x Solving for variable 'x'. Reorder the terms: 6 + -9 + 2x + 7x + -5x2 = 9 + -7x + -9 + 7x Combine like terms: 6 + -9 = -3 -3 + 2x + 7x + -5x2 = 9 + -7x + -9 + 7x Combine like terms: 2x + 7x = 9x -3 + 9x + -5x2 = 9 + -7x + -9 + 7x Reorder the terms: -3 + 9x + -5x2 = 9 + -9 + -7x + 7x Combine like terms: 9 + -9 = 0 -3 + 9x + -5x2 = 0 + -7x + 7x -3 + 9x + -5x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -3 + 9x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.6 + -1.8x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -1.8x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -1.8x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -1.8x + x2 = 0 + -0.6 -1.8x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -1.8x + x2 = -0.6 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = -0.6 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = -0.6 + 0.81 Combine like terms: -0.6 + 0.81 = 0.21 0.81 + -1.8x + x2 = 0.21 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 0.21 Calculate the square root of the right side: 0.458257569 Break this problem into two subproblems by setting (x + -0.9) equal to 0.458257569 and -0.458257569.Subproblem 1
x + -0.9 = 0.458257569 Simplifying x + -0.9 = 0.458257569 Reorder the terms: -0.9 + x = 0.458257569 Solving -0.9 + x = 0.458257569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 0.458257569 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.458257569 + 0.9 x = 0.458257569 + 0.9 Combine like terms: 0.458257569 + 0.9 = 1.358257569 x = 1.358257569 Simplifying x = 1.358257569Subproblem 2
x + -0.9 = -0.458257569 Simplifying x + -0.9 = -0.458257569 Reorder the terms: -0.9 + x = -0.458257569 Solving -0.9 + x = -0.458257569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -0.458257569 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -0.458257569 + 0.9 x = -0.458257569 + 0.9 Combine like terms: -0.458257569 + 0.9 = 0.441742431 x = 0.441742431 Simplifying x = 0.441742431Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.358257569, 0.441742431}
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