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Simplifying 5X2 + -7X = 1.4 Reorder the terms: -7X + 5X2 = 1.4 Solving -7X + 5X2 = 1.4 Solving for variable 'X'. Reorder the terms: -1.4 + -7X + 5X2 = 1.4 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 -1.4 + -7X + 5X2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.28 + -1.4X + X2 = 0.0 Move the constant term to the right: Add '0.28' to each side of the equation. -0.28 + -1.4X + 0.28 + X2 = 0.0 + 0.28 Reorder the terms: -0.28 + 0.28 + -1.4X + X2 = 0.0 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + -1.4X + X2 = 0.0 + 0.28 -1.4X + X2 = 0.0 + 0.28 Combine like terms: 0.0 + 0.28 = 0.28 -1.4X + X2 = 0.28 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 = 0.28 + 0.49 Reorder the terms: 0.49 + -1.4X + X2 = 0.28 + 0.49 Combine like terms: 0.28 + 0.49 = 0.77 0.49 + -1.4X + X2 = 0.77 Factor a perfect square on the left side: (X + -0.7)(X + -0.7) = 0.77 Calculate the square root of the right side: 0.877496439 Break this problem into two subproblems by setting (X + -0.7) equal to 0.877496439 and -0.877496439.Subproblem 1
X + -0.7 = 0.877496439 Simplifying X + -0.7 = 0.877496439 Reorder the terms: -0.7 + X = 0.877496439 Solving -0.7 + X = 0.877496439 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 = 0.877496439 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + X = 0.877496439 + 0.7 X = 0.877496439 + 0.7 Combine like terms: 0.877496439 + 0.7 = 1.577496439 X = 1.577496439 Simplifying X = 1.577496439Subproblem 2
X + -0.7 = -0.877496439 Simplifying X + -0.7 = -0.877496439 Reorder the terms: -0.7 + X = -0.877496439 Solving -0.7 + X = -0.877496439 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 = -0.877496439 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + X = -0.877496439 + 0.7 X = -0.877496439 + 0.7 Combine like terms: -0.877496439 + 0.7 = -0.177496439 X = -0.177496439 Simplifying X = -0.177496439Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.577496439, -0.177496439}
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