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Simplifying x + 5 = ((3x)(3x)) Reorder the terms: 5 + x = ((3x)(3x)) Remove parenthesis around (3x) 5 + x = (3x(3x)) Remove parenthesis around (3x) 5 + x = (3x * 3x) Reorder the terms for easier multiplication: 5 + x = (3 * 3x * x) Multiply 3 * 3 5 + x = (9x * x) Multiply x * x 5 + x = (9x2) Solving 5 + x = (9x2) Solving for variable 'x'. Combine like terms: (9x2) + (-9x2) = 0 5 + x + (-9x2) = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.5555555556 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -0.1111111111x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -0.1111111111x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -0.1111111111x + x2 = 0 + 0.5555555556 -0.1111111111x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -0.1111111111x + x2 = 0.5555555556 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1111111111x + 0.25 + x2 = 0.5555555556 + 0.25 Reorder the terms: 0.25 + -0.1111111111x + x2 = 0.5555555556 + 0.25 Combine like terms: 0.5555555556 + 0.25 = 0.8055555556 0.25 + -0.1111111111x + x2 = 0.8055555556 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 0.8055555556 Calculate the square root of the right side: 0.897527468 Break this problem into two subproblems by setting ((x) + 0.5) equal to 0.897527468 and -0.897527468.Subproblem 1
(x) + 0.5 = 0.897527468 Simplifying (x) + 0.5 = 0.897527468 x + 0.5 = 0.897527468 Reorder the terms: 0.5 + x = 0.897527468 Solving 0.5 + x = 0.897527468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.897527468 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.897527468 + -0.5 x = 0.897527468 + -0.5 Combine like terms: 0.897527468 + -0.5 = 0.397527468 x = 0.397527468 Simplifying x = 0.397527468Subproblem 2
(x) + 0.5 = -0.897527468 Simplifying (x) + 0.5 = -0.897527468 x + 0.5 = -0.897527468 Reorder the terms: 0.5 + x = -0.897527468 Solving 0.5 + x = -0.897527468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.897527468 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.897527468 + -0.5 x = -0.897527468 + -0.5 Combine like terms: -0.897527468 + -0.5 = -1.397527468 x = -1.397527468 Simplifying x = -1.397527468Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.397527468, -1.397527468}
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