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Simplifying 5x2 + -6x = 9x + 1 Reorder the terms: -6x + 5x2 = 9x + 1 Reorder the terms: -6x + 5x2 = 1 + 9x Solving -6x + 5x2 = 1 + 9x Solving for variable 'x'. Reorder the terms: -1 + -6x + -9x + 5x2 = 1 + 9x + -1 + -9x Combine like terms: -6x + -9x = -15x -1 + -15x + 5x2 = 1 + 9x + -1 + -9x Reorder the terms: -1 + -15x + 5x2 = 1 + -1 + 9x + -9x Combine like terms: 1 + -1 = 0 -1 + -15x + 5x2 = 0 + 9x + -9x -1 + -15x + 5x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -1 + -15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -3x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -3x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -3x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -3x + x2 = 0 + 0.2 -3x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -3x + x2 = 0.2 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 = 0.2 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.2 + 2.25 Combine like terms: 0.2 + 2.25 = 2.45 2.25 + -3x + x2 = 2.45 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.45 Calculate the square root of the right side: 1.565247584 Break this problem into two subproblems by setting (x + -1.5) equal to 1.565247584 and -1.565247584.Subproblem 1
x + -1.5 = 1.565247584 Simplifying x + -1.5 = 1.565247584 Reorder the terms: -1.5 + x = 1.565247584 Solving -1.5 + x = 1.565247584 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 = 1.565247584 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.565247584 + 1.5 x = 1.565247584 + 1.5 Combine like terms: 1.565247584 + 1.5 = 3.065247584 x = 3.065247584 Simplifying x = 3.065247584Subproblem 2
x + -1.5 = -1.565247584 Simplifying x + -1.5 = -1.565247584 Reorder the terms: -1.5 + x = -1.565247584 Solving -1.5 + x = -1.565247584 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 = -1.565247584 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.565247584 + 1.5 x = -1.565247584 + 1.5 Combine like terms: -1.565247584 + 1.5 = -0.065247584 x = -0.065247584 Simplifying x = -0.065247584Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.065247584, -0.065247584}
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