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Simplifying 4x2 = 18x + 18 Reorder the terms: 4x2 = 18 + 18x Solving 4x2 = 18 + 18x Solving for variable 'x'. Reorder the terms: -18 + -18x + 4x2 = 18 + 18x + -18 + -18x Reorder the terms: -18 + -18x + 4x2 = 18 + -18 + 18x + -18x Combine like terms: 18 + -18 = 0 -18 + -18x + 4x2 = 0 + 18x + -18x -18 + -18x + 4x2 = 18x + -18x Combine like terms: 18x + -18x = 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 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 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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