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Simplifying 18x + 6x2 = 300 Solving 18x + 6x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 18x + 6x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 18x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-50 + 3x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-50 + 3x + x2)' equal to zero and attempt to solve: Simplifying -50 + 3x + x2 = 0 Solving -50 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 3x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 3x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 3x + x2 = 0 + 50 3x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 3x + x2 = 50 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 = 50 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 50 + 2.25 Combine like terms: 50 + 2.25 = 52.25 2.25 + 3x + x2 = 52.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + 1.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + 1.5 = 7.228416147 Simplifying x + 1.5 = 7.228416147 Reorder the terms: 1.5 + x = 7.228416147 Solving 1.5 + x = 7.228416147 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 = 7.228416147 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.228416147 + -1.5 x = 7.228416147 + -1.5 Combine like terms: 7.228416147 + -1.5 = 5.728416147 x = 5.728416147 Simplifying x = 5.728416147Subproblem 2
x + 1.5 = -7.228416147 Simplifying x + 1.5 = -7.228416147 Reorder the terms: 1.5 + x = -7.228416147 Solving 1.5 + x = -7.228416147 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 = -7.228416147 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.228416147 + -1.5 x = -7.228416147 + -1.5 Combine like terms: -7.228416147 + -1.5 = -8.728416147 x = -8.728416147 Simplifying x = -8.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.728416147, -8.728416147}Solution
x = {5.728416147, -8.728416147}
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