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Simplifying 4x2 + 40x + 18 = 0 Reorder the terms: 18 + 40x + 4x2 = 0 Solving 18 + 40x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 20x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 20x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + 20x + 2x2 = 0 Solving 9 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 10x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 10x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 10x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 10x + x2 = 0 + -4.5 10x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 10x + x2 = -4.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -4.5 + 25 Reorder the terms: 25 + 10x + x2 = -4.5 + 25 Combine like terms: -4.5 + 25 = 20.5 25 + 10x + x2 = 20.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (x + 5) equal to 4.527692569 and -4.527692569.Subproblem 1
x + 5 = 4.527692569 Simplifying x + 5 = 4.527692569 Reorder the terms: 5 + x = 4.527692569 Solving 5 + x = 4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.527692569 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.527692569 + -5 x = 4.527692569 + -5 Combine like terms: 4.527692569 + -5 = -0.472307431 x = -0.472307431 Simplifying x = -0.472307431Subproblem 2
x + 5 = -4.527692569 Simplifying x + 5 = -4.527692569 Reorder the terms: 5 + x = -4.527692569 Solving 5 + x = -4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.527692569 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.527692569 + -5 x = -4.527692569 + -5 Combine like terms: -4.527692569 + -5 = -9.527692569 x = -9.527692569 Simplifying x = -9.527692569Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.472307431, -9.527692569}Solution
x = {-0.472307431, -9.527692569}
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