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Simplifying x2 + -3.2x + -3.56 = 0 Reorder the terms: -3.56 + -3.2x + x2 = 0 Solving -3.56 + -3.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3.56' to each side of the equation. -3.56 + -3.2x + 3.56 + x2 = 0 + 3.56 Reorder the terms: -3.56 + 3.56 + -3.2x + x2 = 0 + 3.56 Combine like terms: -3.56 + 3.56 = 0.00 0.00 + -3.2x + x2 = 0 + 3.56 -3.2x + x2 = 0 + 3.56 Combine like terms: 0 + 3.56 = 3.56 -3.2x + x2 = 3.56 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 3.56 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 3.56 + 2.56 Combine like terms: 3.56 + 2.56 = 6.12 2.56 + -3.2x + x2 = 6.12 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 6.12 Calculate the square root of the right side: 2.473863375 Break this problem into two subproblems by setting (x + -1.6) equal to 2.473863375 and -2.473863375.Subproblem 1
x + -1.6 = 2.473863375 Simplifying x + -1.6 = 2.473863375 Reorder the terms: -1.6 + x = 2.473863375 Solving -1.6 + x = 2.473863375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 2.473863375 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 2.473863375 + 1.6 x = 2.473863375 + 1.6 Combine like terms: 2.473863375 + 1.6 = 4.073863375 x = 4.073863375 Simplifying x = 4.073863375Subproblem 2
x + -1.6 = -2.473863375 Simplifying x + -1.6 = -2.473863375 Reorder the terms: -1.6 + x = -2.473863375 Solving -1.6 + x = -2.473863375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -2.473863375 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -2.473863375 + 1.6 x = -2.473863375 + 1.6 Combine like terms: -2.473863375 + 1.6 = -0.873863375 x = -0.873863375 Simplifying x = -0.873863375Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.073863375, -0.873863375}
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