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Simplifying 2x2 + -18x + 5 = 3 Reorder the terms: 5 + -18x + 2x2 = 3 Solving 5 + -18x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: 5 + -3 + -18x + 2x2 = 3 + -3 Combine like terms: 5 + -3 = 2 2 + -18x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 2 + -18x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -9x + x2)' equal to zero and attempt to solve: Simplifying 1 + -9x + x2 = 0 Solving 1 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -9x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -9x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9x + x2 = 0 + -1 -9x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -9x + x2 = -1 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -1 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -1 + 20.25 Combine like terms: -1 + 20.25 = 19.25 20.25 + -9x + x2 = 19.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + -4.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + -4.5 = 4.387482194 Simplifying x + -4.5 = 4.387482194 Reorder the terms: -4.5 + x = 4.387482194 Solving -4.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.387482194 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.387482194 + 4.5 x = 4.387482194 + 4.5 Combine like terms: 4.387482194 + 4.5 = 8.887482194 x = 8.887482194 Simplifying x = 8.887482194Subproblem 2
x + -4.5 = -4.387482194 Simplifying x + -4.5 = -4.387482194 Reorder the terms: -4.5 + x = -4.387482194 Solving -4.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.387482194 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.387482194 + 4.5 x = -4.387482194 + 4.5 Combine like terms: -4.387482194 + 4.5 = 0.112517806 x = 0.112517806 Simplifying x = 0.112517806Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.887482194, 0.112517806}Solution
x = {8.887482194, 0.112517806}
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