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Simplifying 4X2 + 2.8X + -1.371 = 0 Reorder the terms: -1.371 + 2.8X + 4X2 = 0 Solving -1.371 + 2.8X + 4X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.34275 + 0.7X + X2 = 0 Move the constant term to the right: Add '0.34275' to each side of the equation. -0.34275 + 0.7X + 0.34275 + X2 = 0 + 0.34275 Reorder the terms: -0.34275 + 0.34275 + 0.7X + X2 = 0 + 0.34275 Combine like terms: -0.34275 + 0.34275 = 0.00000 0.00000 + 0.7X + X2 = 0 + 0.34275 0.7X + X2 = 0 + 0.34275 Combine like terms: 0 + 0.34275 = 0.34275 0.7X + X2 = 0.34275 The X term is 0.7X. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7X + 0.1225 + X2 = 0.34275 + 0.1225 Reorder the terms: 0.1225 + 0.7X + X2 = 0.34275 + 0.1225 Combine like terms: 0.34275 + 0.1225 = 0.46525 0.1225 + 0.7X + X2 = 0.46525 Factor a perfect square on the left side: (X + 0.35)(X + 0.35) = 0.46525 Calculate the square root of the right side: 0.682092369 Break this problem into two subproblems by setting (X + 0.35) equal to 0.682092369 and -0.682092369.Subproblem 1
X + 0.35 = 0.682092369 Simplifying X + 0.35 = 0.682092369 Reorder the terms: 0.35 + X = 0.682092369 Solving 0.35 + X = 0.682092369 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + X = 0.682092369 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + X = 0.682092369 + -0.35 X = 0.682092369 + -0.35 Combine like terms: 0.682092369 + -0.35 = 0.332092369 X = 0.332092369 Simplifying X = 0.332092369Subproblem 2
X + 0.35 = -0.682092369 Simplifying X + 0.35 = -0.682092369 Reorder the terms: 0.35 + X = -0.682092369 Solving 0.35 + X = -0.682092369 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + X = -0.682092369 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + X = -0.682092369 + -0.35 X = -0.682092369 + -0.35 Combine like terms: -0.682092369 + -0.35 = -1.032092369 X = -1.032092369 Simplifying X = -1.032092369Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.332092369, -1.032092369}
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