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Simplifying 2.25x2 + -8x + 7 = 0 Reorder the terms: 7 + -8x + 2.25x2 = 0 Solving 7 + -8x + 2.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.25 the coefficient of the squared term: Divide each side by '2.25'. 3.111111111 + -3.555555556x + x2 = 0 Move the constant term to the right: Add '-3.111111111' to each side of the equation. 3.111111111 + -3.555555556x + -3.111111111 + x2 = 0 + -3.111111111 Reorder the terms: 3.111111111 + -3.111111111 + -3.555555556x + x2 = 0 + -3.111111111 Combine like terms: 3.111111111 + -3.111111111 = 0.000000000 0.000000000 + -3.555555556x + x2 = 0 + -3.111111111 -3.555555556x + x2 = 0 + -3.111111111 Combine like terms: 0 + -3.111111111 = -3.111111111 -3.555555556x + x2 = -3.111111111 The x term is -3.555555556x. Take half its coefficient (-1.777777778). Square it (3.160493828) and add it to both sides. Add '3.160493828' to each side of the equation. -3.555555556x + 3.160493828 + x2 = -3.111111111 + 3.160493828 Reorder the terms: 3.160493828 + -3.555555556x + x2 = -3.111111111 + 3.160493828 Combine like terms: -3.111111111 + 3.160493828 = 0.049382717 3.160493828 + -3.555555556x + x2 = 0.049382717 Factor a perfect square on the left side: (x + -1.777777778)(x + -1.777777778) = 0.049382717 Calculate the square root of the right side: 0.222222224 Break this problem into two subproblems by setting (x + -1.777777778) equal to 0.222222224 and -0.222222224.Subproblem 1
x + -1.777777778 = 0.222222224 Simplifying x + -1.777777778 = 0.222222224 Reorder the terms: -1.777777778 + x = 0.222222224 Solving -1.777777778 + x = 0.222222224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.777777778' to each side of the equation. -1.777777778 + 1.777777778 + x = 0.222222224 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + x = 0.222222224 + 1.777777778 x = 0.222222224 + 1.777777778 Combine like terms: 0.222222224 + 1.777777778 = 2.000000002 x = 2.000000002 Simplifying x = 2.000000002Subproblem 2
x + -1.777777778 = -0.222222224 Simplifying x + -1.777777778 = -0.222222224 Reorder the terms: -1.777777778 + x = -0.222222224 Solving -1.777777778 + x = -0.222222224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.777777778' to each side of the equation. -1.777777778 + 1.777777778 + x = -0.222222224 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + x = -0.222222224 + 1.777777778 x = -0.222222224 + 1.777777778 Combine like terms: -0.222222224 + 1.777777778 = 1.555555554 x = 1.555555554 Simplifying x = 1.555555554Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.000000002, 1.555555554}
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