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Simplifying 6x + 18 = 4x2 + x2 Reorder the terms: 18 + 6x = 4x2 + x2 Combine like terms: 4x2 + x2 = 5x2 18 + 6x = 5x2 Solving 18 + 6x = 5x2 Solving for variable 'x'. Combine like terms: 5x2 + -5x2 = 0 18 + 6x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.6 + -1.2x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -1.2x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -1.2x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -1.2x + x2 = 0 + 3.6 -1.2x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -1.2x + x2 = 3.6 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 3.6 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 3.6 + 0.36 Combine like terms: 3.6 + 0.36 = 3.96 0.36 + -1.2x + x2 = 3.96 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 3.96 Calculate the square root of the right side: 1.989974874 Break this problem into two subproblems by setting (x + -0.6) equal to 1.989974874 and -1.989974874.Subproblem 1
x + -0.6 = 1.989974874 Simplifying x + -0.6 = 1.989974874 Reorder the terms: -0.6 + x = 1.989974874 Solving -0.6 + x = 1.989974874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.989974874 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.989974874 + 0.6 x = 1.989974874 + 0.6 Combine like terms: 1.989974874 + 0.6 = 2.589974874 x = 2.589974874 Simplifying x = 2.589974874Subproblem 2
x + -0.6 = -1.989974874 Simplifying x + -0.6 = -1.989974874 Reorder the terms: -0.6 + x = -1.989974874 Solving -0.6 + x = -1.989974874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.989974874 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.989974874 + 0.6 x = -1.989974874 + 0.6 Combine like terms: -1.989974874 + 0.6 = -1.389974874 x = -1.389974874 Simplifying x = -1.389974874Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.589974874, -1.389974874}
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