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Simplifying x2 + -2.6x + 0.56 = 0 Reorder the terms: 0.56 + -2.6x + x2 = 0 Solving 0.56 + -2.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.56' to each side of the equation. 0.56 + -2.6x + -0.56 + x2 = 0 + -0.56 Reorder the terms: 0.56 + -0.56 + -2.6x + x2 = 0 + -0.56 Combine like terms: 0.56 + -0.56 = 0.00 0.00 + -2.6x + x2 = 0 + -0.56 -2.6x + x2 = 0 + -0.56 Combine like terms: 0 + -0.56 = -0.56 -2.6x + x2 = -0.56 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = -0.56 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = -0.56 + 1.69 Combine like terms: -0.56 + 1.69 = 1.13 1.69 + -2.6x + x2 = 1.13 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 1.13 Calculate the square root of the right side: 1.063014581 Break this problem into two subproblems by setting (x + -1.3) equal to 1.063014581 and -1.063014581.Subproblem 1
x + -1.3 = 1.063014581 Simplifying x + -1.3 = 1.063014581 Reorder the terms: -1.3 + x = 1.063014581 Solving -1.3 + x = 1.063014581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 1.063014581 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 1.063014581 + 1.3 x = 1.063014581 + 1.3 Combine like terms: 1.063014581 + 1.3 = 2.363014581 x = 2.363014581 Simplifying x = 2.363014581Subproblem 2
x + -1.3 = -1.063014581 Simplifying x + -1.3 = -1.063014581 Reorder the terms: -1.3 + x = -1.063014581 Solving -1.3 + x = -1.063014581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = -1.063014581 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -1.063014581 + 1.3 x = -1.063014581 + 1.3 Combine like terms: -1.063014581 + 1.3 = 0.236985419 x = 0.236985419 Simplifying x = 0.236985419Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.363014581, 0.236985419}
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