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Simplifying 4x2 + -2.8x + -5.7 = 0 Reorder the terms: -5.7 + -2.8x + 4x2 = 0 Solving -5.7 + -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'. -1.425 + -0.7x + x2 = 0 Move the constant term to the right: Add '1.425' to each side of the equation. -1.425 + -0.7x + 1.425 + x2 = 0 + 1.425 Reorder the terms: -1.425 + 1.425 + -0.7x + x2 = 0 + 1.425 Combine like terms: -1.425 + 1.425 = 0.000 0.000 + -0.7x + x2 = 0 + 1.425 -0.7x + x2 = 0 + 1.425 Combine like terms: 0 + 1.425 = 1.425 -0.7x + x2 = 1.425 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 = 1.425 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 1.425 + 0.1225 Combine like terms: 1.425 + 0.1225 = 1.5475 0.1225 + -0.7x + x2 = 1.5475 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 1.5475 Calculate the square root of the right side: 1.24398553 Break this problem into two subproblems by setting (x + -0.35) equal to 1.24398553 and -1.24398553.Subproblem 1
x + -0.35 = 1.24398553 Simplifying x + -0.35 = 1.24398553 Reorder the terms: -0.35 + x = 1.24398553 Solving -0.35 + x = 1.24398553 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 = 1.24398553 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 1.24398553 + 0.35 x = 1.24398553 + 0.35 Combine like terms: 1.24398553 + 0.35 = 1.59398553 x = 1.59398553 Simplifying x = 1.59398553Subproblem 2
x + -0.35 = -1.24398553 Simplifying x + -0.35 = -1.24398553 Reorder the terms: -0.35 + x = -1.24398553 Solving -0.35 + x = -1.24398553 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 = -1.24398553 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -1.24398553 + 0.35 x = -1.24398553 + 0.35 Combine like terms: -1.24398553 + 0.35 = -0.89398553 x = -0.89398553 Simplifying x = -0.89398553Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.59398553, -0.89398553}
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