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Simplifying x2 + -4.5x + 2.6 = 0 Reorder the terms: 2.6 + -4.5x + x2 = 0 Solving 2.6 + -4.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + -4.5x + -2.6 + x2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + -4.5x + x2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + -4.5x + x2 = 0 + -2.6 -4.5x + x2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 -4.5x + x2 = -2.6 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -2.6 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -2.6 + 5.0625 Combine like terms: -2.6 + 5.0625 = 2.4625 5.0625 + -4.5x + x2 = 2.4625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 2.4625 Calculate the square root of the right side: 1.569235483 Break this problem into two subproblems by setting (x + -2.25) equal to 1.569235483 and -1.569235483.Subproblem 1
x + -2.25 = 1.569235483 Simplifying x + -2.25 = 1.569235483 Reorder the terms: -2.25 + x = 1.569235483 Solving -2.25 + x = 1.569235483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.569235483 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.569235483 + 2.25 x = 1.569235483 + 2.25 Combine like terms: 1.569235483 + 2.25 = 3.819235483 x = 3.819235483 Simplifying x = 3.819235483Subproblem 2
x + -2.25 = -1.569235483 Simplifying x + -2.25 = -1.569235483 Reorder the terms: -2.25 + x = -1.569235483 Solving -2.25 + x = -1.569235483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.569235483 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.569235483 + 2.25 x = -1.569235483 + 2.25 Combine like terms: -1.569235483 + 2.25 = 0.680764517 x = 0.680764517 Simplifying x = 0.680764517Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.819235483, 0.680764517}
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