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Simplifying 5x2 + 18x = 18 + -6x Reorder the terms: 18x + 5x2 = 18 + -6x Solving 18x + 5x2 = 18 + -6x Solving for variable 'x'. Reorder the terms: -18 + 18x + 6x + 5x2 = 18 + -6x + -18 + 6x Combine like terms: 18x + 6x = 24x -18 + 24x + 5x2 = 18 + -6x + -18 + 6x Reorder the terms: -18 + 24x + 5x2 = 18 + -18 + -6x + 6x Combine like terms: 18 + -18 = 0 -18 + 24x + 5x2 = 0 + -6x + 6x -18 + 24x + 5x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -18 + 24x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + 4.8x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 4.8x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 4.8x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 4.8x + x2 = 0 + 3.6 4.8x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 4.8x + x2 = 3.6 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = 3.6 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 3.6 + 5.76 Combine like terms: 3.6 + 5.76 = 9.36 5.76 + 4.8x + x2 = 9.36 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 9.36 Calculate the square root of the right side: 3.059411708 Break this problem into two subproblems by setting (x + 2.4) equal to 3.059411708 and -3.059411708.Subproblem 1
x + 2.4 = 3.059411708 Simplifying x + 2.4 = 3.059411708 Reorder the terms: 2.4 + x = 3.059411708 Solving 2.4 + x = 3.059411708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 3.059411708 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 3.059411708 + -2.4 x = 3.059411708 + -2.4 Combine like terms: 3.059411708 + -2.4 = 0.659411708 x = 0.659411708 Simplifying x = 0.659411708Subproblem 2
x + 2.4 = -3.059411708 Simplifying x + 2.4 = -3.059411708 Reorder the terms: 2.4 + x = -3.059411708 Solving 2.4 + x = -3.059411708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -3.059411708 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -3.059411708 + -2.4 x = -3.059411708 + -2.4 Combine like terms: -3.059411708 + -2.4 = -5.459411708 x = -5.459411708 Simplifying x = -5.459411708Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.659411708, -5.459411708}
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