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Simplifying -4.9x2 + 2.25x + 2 = 0 Reorder the terms: 2 + 2.25x + -4.9x2 = 0 Solving 2 + 2.25x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.4081632653 + -0.4591836735x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -0.4591836735x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -0.4591836735x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -0.4591836735x + x2 = 0 + 0.4081632653 -0.4591836735x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -0.4591836735x + x2 = 0.4081632653 The x term is -0.4591836735x. Take half its coefficient (-0.2295918368). Square it (0.05271241153) and add it to both sides. Add '0.05271241153' to each side of the equation. -0.4591836735x + 0.05271241153 + x2 = 0.4081632653 + 0.05271241153 Reorder the terms: 0.05271241153 + -0.4591836735x + x2 = 0.4081632653 + 0.05271241153 Combine like terms: 0.4081632653 + 0.05271241153 = 0.46087567683 0.05271241153 + -0.4591836735x + x2 = 0.46087567683 Factor a perfect square on the left side: (x + -0.2295918368)(x + -0.2295918368) = 0.46087567683 Calculate the square root of the right side: 0.678878249 Break this problem into two subproblems by setting (x + -0.2295918368) equal to 0.678878249 and -0.678878249.Subproblem 1
x + -0.2295918368 = 0.678878249 Simplifying x + -0.2295918368 = 0.678878249 Reorder the terms: -0.2295918368 + x = 0.678878249 Solving -0.2295918368 + x = 0.678878249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2295918368' to each side of the equation. -0.2295918368 + 0.2295918368 + x = 0.678878249 + 0.2295918368 Combine like terms: -0.2295918368 + 0.2295918368 = 0.0000000000 0.0000000000 + x = 0.678878249 + 0.2295918368 x = 0.678878249 + 0.2295918368 Combine like terms: 0.678878249 + 0.2295918368 = 0.9084700858 x = 0.9084700858 Simplifying x = 0.9084700858Subproblem 2
x + -0.2295918368 = -0.678878249 Simplifying x + -0.2295918368 = -0.678878249 Reorder the terms: -0.2295918368 + x = -0.678878249 Solving -0.2295918368 + x = -0.678878249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2295918368' to each side of the equation. -0.2295918368 + 0.2295918368 + x = -0.678878249 + 0.2295918368 Combine like terms: -0.2295918368 + 0.2295918368 = 0.0000000000 0.0000000000 + x = -0.678878249 + 0.2295918368 x = -0.678878249 + 0.2295918368 Combine like terms: -0.678878249 + 0.2295918368 = -0.4492864122 x = -0.4492864122 Simplifying x = -0.4492864122Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9084700858, -0.4492864122}
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