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Simplifying 5X2 + -7X + -15 = 0 Reorder the terms: -15 + -7X + 5X2 = 0 Solving -15 + -7X + 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'. -3 + -1.4X + X2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.4X + 3 + X2 = 0 + 3 Reorder the terms: -3 + 3 + -1.4X + X2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.4X + X2 = 0 + 3 -1.4X + X2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.4X + X2 = 3 The X term is -1.4X. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4X + 0.49 + X2 = 3 + 0.49 Reorder the terms: 0.49 + -1.4X + X2 = 3 + 0.49 Combine like terms: 3 + 0.49 = 3.49 0.49 + -1.4X + X2 = 3.49 Factor a perfect square on the left side: (X + -0.7)(X + -0.7) = 3.49 Calculate the square root of the right side: 1.868154169 Break this problem into two subproblems by setting (X + -0.7) equal to 1.868154169 and -1.868154169.Subproblem 1
X + -0.7 = 1.868154169 Simplifying X + -0.7 = 1.868154169 Reorder the terms: -0.7 + X = 1.868154169 Solving -0.7 + X = 1.868154169 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + X = 1.868154169 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + X = 1.868154169 + 0.7 X = 1.868154169 + 0.7 Combine like terms: 1.868154169 + 0.7 = 2.568154169 X = 2.568154169 Simplifying X = 2.568154169Subproblem 2
X + -0.7 = -1.868154169 Simplifying X + -0.7 = -1.868154169 Reorder the terms: -0.7 + X = -1.868154169 Solving -0.7 + X = -1.868154169 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + X = -1.868154169 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + X = -1.868154169 + 0.7 X = -1.868154169 + 0.7 Combine like terms: -1.868154169 + 0.7 = -1.168154169 X = -1.168154169 Simplifying X = -1.168154169Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.568154169, -1.168154169}
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