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Simplifying 2x2 + 6x + -600 = 0 Reorder the terms: -600 + 6x + 2x2 = 0 Solving -600 + 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-300 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-300 + 3x + x2)' equal to zero and attempt to solve: Simplifying -300 + 3x + x2 = 0 Solving -300 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 3x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 3x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 3x + x2 = 0 + 300 3x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 3x + x2 = 300 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 300 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 300 + 2.25 Combine like terms: 300 + 2.25 = 302.25 2.25 + 3x + x2 = 302.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 302.25 Calculate the square root of the right side: 17.385338651 Break this problem into two subproblems by setting (x + 1.5) equal to 17.385338651 and -17.385338651.Subproblem 1
x + 1.5 = 17.385338651 Simplifying x + 1.5 = 17.385338651 Reorder the terms: 1.5 + x = 17.385338651 Solving 1.5 + x = 17.385338651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 17.385338651 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 17.385338651 + -1.5 x = 17.385338651 + -1.5 Combine like terms: 17.385338651 + -1.5 = 15.885338651 x = 15.885338651 Simplifying x = 15.885338651Subproblem 2
x + 1.5 = -17.385338651 Simplifying x + 1.5 = -17.385338651 Reorder the terms: 1.5 + x = -17.385338651 Solving 1.5 + x = -17.385338651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -17.385338651 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -17.385338651 + -1.5 x = -17.385338651 + -1.5 Combine like terms: -17.385338651 + -1.5 = -18.885338651 x = -18.885338651 Simplifying x = -18.885338651Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.885338651, -18.885338651}Solution
x = {15.885338651, -18.885338651}
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