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Simplifying -1 + 5x(x + -2) = 12x + 3 + -7x Reorder the terms: -1 + 5x(-2 + x) = 12x + 3 + -7x -1 + (-2 * 5x + x * 5x) = 12x + 3 + -7x -1 + (-10x + 5x2) = 12x + 3 + -7x Reorder the terms: -1 + -10x + 5x2 = 3 + 12x + -7x Combine like terms: 12x + -7x = 5x -1 + -10x + 5x2 = 3 + 5x Solving -1 + -10x + 5x2 = 3 + 5x Solving for variable 'x'. Reorder the terms: -1 + -3 + -10x + -5x + 5x2 = 3 + 5x + -3 + -5x Combine like terms: -1 + -3 = -4 -4 + -10x + -5x + 5x2 = 3 + 5x + -3 + -5x Combine like terms: -10x + -5x = -15x -4 + -15x + 5x2 = 3 + 5x + -3 + -5x Reorder the terms: -4 + -15x + 5x2 = 3 + -3 + 5x + -5x Combine like terms: 3 + -3 = 0 -4 + -15x + 5x2 = 0 + 5x + -5x -4 + -15x + 5x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -4 + -15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -3x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -3x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -3x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -3x + x2 = 0 + 0.8 -3x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -3x + x2 = 0.8 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 = 0.8 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.8 + 2.25 Combine like terms: 0.8 + 2.25 = 3.05 2.25 + -3x + x2 = 3.05 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 3.05 Calculate the square root of the right side: 1.74642492 Break this problem into two subproblems by setting (x + -1.5) equal to 1.74642492 and -1.74642492.Subproblem 1
x + -1.5 = 1.74642492 Simplifying x + -1.5 = 1.74642492 Reorder the terms: -1.5 + x = 1.74642492 Solving -1.5 + x = 1.74642492 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 = 1.74642492 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.74642492 + 1.5 x = 1.74642492 + 1.5 Combine like terms: 1.74642492 + 1.5 = 3.24642492 x = 3.24642492 Simplifying x = 3.24642492Subproblem 2
x + -1.5 = -1.74642492 Simplifying x + -1.5 = -1.74642492 Reorder the terms: -1.5 + x = -1.74642492 Solving -1.5 + x = -1.74642492 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 = -1.74642492 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.74642492 + 1.5 x = -1.74642492 + 1.5 Combine like terms: -1.74642492 + 1.5 = -0.24642492 x = -0.24642492 Simplifying x = -0.24642492Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.24642492, -0.24642492}
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