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Simplifying 4x2 + 18x = 34 Reorder the terms: 18x + 4x2 = 34 Solving 18x + 4x2 = 34 Solving for variable 'x'. Reorder the terms: -34 + 18x + 4x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 18x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + 9x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying -17 + 9x + 2x2 = 0 Solving -17 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + 4.5x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + 4.5x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + 4.5x + x2 = 0 + 8.5 4.5x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 4.5x + x2 = 8.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 8.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 8.5 + 5.0625 Combine like terms: 8.5 + 5.0625 = 13.5625 5.0625 + 4.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + 2.25) equal to 3.682729966 and -3.682729966.Subproblem 1
x + 2.25 = 3.682729966 Simplifying x + 2.25 = 3.682729966 Reorder the terms: 2.25 + x = 3.682729966 Solving 2.25 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.682729966 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.682729966 + -2.25 x = 3.682729966 + -2.25 Combine like terms: 3.682729966 + -2.25 = 1.432729966 x = 1.432729966 Simplifying x = 1.432729966Subproblem 2
x + 2.25 = -3.682729966 Simplifying x + 2.25 = -3.682729966 Reorder the terms: 2.25 + x = -3.682729966 Solving 2.25 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.682729966 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.682729966 + -2.25 x = -3.682729966 + -2.25 Combine like terms: -3.682729966 + -2.25 = -5.932729966 x = -5.932729966 Simplifying x = -5.932729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.432729966, -5.932729966}Solution
x = {1.432729966, -5.932729966}
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