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Simplifying 6x + 18 = (4x2) + -12x Reorder the terms: 18 + 6x = (4x2) + -12x Reorder the terms: 18 + 6x = -12x + (4x2) Solving 18 + 6x = -12x + (4x2) Solving for variable 'x'. Combine like terms: 6x + 12x = 18x 18 + 18x + (-4x2) = -12x + (4x2) + 12x + (-4x2) Reorder the terms: 18 + 18x + (-4x2) = -12x + 12x + (4x2) + (-4x2) Combine like terms: -12x + 12x = 0 18 + 18x + (-4x2) = 0 + (4x2) + (-4x2) 18 + 18x + (-4x2) = (4x2) + (-4x2) Combine like terms: (4x2) + (-4x2) = 0 18 + 18x + (-4x2) = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 9x + (-2x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 9x + (-2x2))' equal to zero and attempt to solve: Simplifying 9 + 9x + (-2x2) = 0 Solving 9 + 9x + (-2x2) = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -4.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -4.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -4.5x + x2 = 0 + 4.5 -4.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -4.5x + x2 = 4.5 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 = 4.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 4.5 + 5.0625 Combine like terms: 4.5 + 5.0625 = 9.5625 5.0625 + -4.5x + x2 = 9.5625 Factor a perfect square on the left side: ((x) + -2.25)((x) + -2.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting ((x) + -2.25) equal to 3.092329219 and -3.092329219.Subproblem 1
(x) + -2.25 = 3.092329219 Simplifying (x) + -2.25 = 3.092329219 x + -2.25 = 3.092329219 Reorder the terms: -2.25 + x = 3.092329219 Solving -2.25 + x = 3.092329219 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 = 3.092329219 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 3.092329219 + 2.25 x = 3.092329219 + 2.25 Combine like terms: 3.092329219 + 2.25 = 5.342329219 x = 5.342329219 Simplifying x = 5.342329219Subproblem 2
(x) + -2.25 = -3.092329219 Simplifying (x) + -2.25 = -3.092329219 x + -2.25 = -3.092329219 Reorder the terms: -2.25 + x = -3.092329219 Solving -2.25 + x = -3.092329219 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 = -3.092329219 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -3.092329219 + 2.25 x = -3.092329219 + 2.25 Combine like terms: -3.092329219 + 2.25 = -0.842329219 x = -0.842329219 Simplifying x = -0.842329219Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.342329219, -0.842329219}Solution
x = {5.342329219, -0.842329219}
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