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Simplifying 5X2 + 15X + 4 = 0 Reorder the terms: 4 + 15X + 5X2 = 0 Solving 4 + 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'. 0.8 + 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 = 1.45 2.25 + 3X + X2 = 1.45 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (X + 1.5) equal to 1.204159458 and -1.204159458.Subproblem 1
X + 1.5 = 1.204159458 Simplifying X + 1.5 = 1.204159458 Reorder the terms: 1.5 + X = 1.204159458 Solving 1.5 + X = 1.204159458 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 = 1.204159458 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 1.204159458 + -1.5 X = 1.204159458 + -1.5 Combine like terms: 1.204159458 + -1.5 = -0.295840542 X = -0.295840542 Simplifying X = -0.295840542Subproblem 2
X + 1.5 = -1.204159458 Simplifying X + 1.5 = -1.204159458 Reorder the terms: 1.5 + X = -1.204159458 Solving 1.5 + X = -1.204159458 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 = -1.204159458 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -1.204159458 + -1.5 X = -1.204159458 + -1.5 Combine like terms: -1.204159458 + -1.5 = -2.704159458 X = -2.704159458 Simplifying X = -2.704159458Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.295840542, -2.704159458}
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