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Simplifying (-5x * x) + -15x + 1 = 0 Multiply x * x (-5x2) + -15x + 1 = 0 Reorder the terms: 1 + -15x + (-5x2) = 0 Solving 1 + -15x + (-5x2) = 0 Solving for variable 'x'. 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 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 = 0.065247584Subproblem 2
(x) + 1.5 = -1.565247584 Simplifying (x) + 1.5 = -1.565247584 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 = -3.065247584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.065247584, -3.065247584}
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