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Simplifying 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 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 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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