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Simplifying 4x2 + 20x + -34 = 0 Reorder the terms: -34 + 20x + 4x2 = 0 Solving -34 + 20x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + 10x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + 10x + 2x2)' equal to zero and attempt to solve: Simplifying -17 + 10x + 2x2 = 0 Solving -17 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + 5x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + 5x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + 5x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + 5x + x2 = 0 + 8.5 5x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 5x + x2 = 8.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 8.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 8.5 + 6.25 Combine like terms: 8.5 + 6.25 = 14.75 6.25 + 5x + x2 = 14.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 14.75 Calculate the square root of the right side: 3.840572874 Break this problem into two subproblems by setting (x + 2.5) equal to 3.840572874 and -3.840572874.Subproblem 1
x + 2.5 = 3.840572874 Simplifying x + 2.5 = 3.840572874 Reorder the terms: 2.5 + x = 3.840572874 Solving 2.5 + x = 3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.840572874 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.840572874 + -2.5 x = 3.840572874 + -2.5 Combine like terms: 3.840572874 + -2.5 = 1.340572874 x = 1.340572874 Simplifying x = 1.340572874Subproblem 2
x + 2.5 = -3.840572874 Simplifying x + 2.5 = -3.840572874 Reorder the terms: 2.5 + x = -3.840572874 Solving 2.5 + x = -3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.840572874 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.840572874 + -2.5 x = -3.840572874 + -2.5 Combine like terms: -3.840572874 + -2.5 = -6.340572874 x = -6.340572874 Simplifying x = -6.340572874Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.340572874, -6.340572874}Solution
x = {1.340572874, -6.340572874}
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