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Simplifying 18x2 + 18x + -10 = 0 Reorder the terms: -10 + 18x + 18x2 = 0 Solving -10 + 18x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 9x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 9x + 9x2)' equal to zero and attempt to solve: Simplifying -5 + 9x + 9x2 = 0 Solving -5 + 9x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.5555555556 x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 x + 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. + 0.25 + x2 = 0.5555555556 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.5555555556 + 0.25 Combine like terms: 0.5555555556 + 0.25 = 0.8055555556 1.25 + 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 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 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}Solution
x = {0.397527468, -1.397527468}
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