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Simplifying 5x2 + 18x = 112 Reorder the terms: 18x + 5x2 = 112 Solving 18x + 5x2 = 112 Solving for variable 'x'. Reorder the terms: -112 + 18x + 5x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + 18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -22.4 + 3.6x + x2 = 0 Move the constant term to the right: Add '22.4' to each side of the equation. -22.4 + 3.6x + 22.4 + x2 = 0 + 22.4 Reorder the terms: -22.4 + 22.4 + 3.6x + x2 = 0 + 22.4 Combine like terms: -22.4 + 22.4 = 0.0 0.0 + 3.6x + x2 = 0 + 22.4 3.6x + x2 = 0 + 22.4 Combine like terms: 0 + 22.4 = 22.4 3.6x + x2 = 22.4 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 22.4 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 22.4 + 3.24 Combine like terms: 22.4 + 3.24 = 25.64 3.24 + 3.6x + x2 = 25.64 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 25.64 Calculate the square root of the right side: 5.06359556 Break this problem into two subproblems by setting (x + 1.8) equal to 5.06359556 and -5.06359556.Subproblem 1
x + 1.8 = 5.06359556 Simplifying x + 1.8 = 5.06359556 Reorder the terms: 1.8 + x = 5.06359556 Solving 1.8 + x = 5.06359556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 5.06359556 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 5.06359556 + -1.8 x = 5.06359556 + -1.8 Combine like terms: 5.06359556 + -1.8 = 3.26359556 x = 3.26359556 Simplifying x = 3.26359556Subproblem 2
x + 1.8 = -5.06359556 Simplifying x + 1.8 = -5.06359556 Reorder the terms: 1.8 + x = -5.06359556 Solving 1.8 + x = -5.06359556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -5.06359556 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -5.06359556 + -1.8 x = -5.06359556 + -1.8 Combine like terms: -5.06359556 + -1.8 = -6.86359556 x = -6.86359556 Simplifying x = -6.86359556Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.26359556, -6.86359556}
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