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Simplifying 12x + 2.5x2 = 162 Solving 12x + 2.5x2 = 162 Solving for variable 'x'. Reorder the terms: -162 + 12x + 2.5x2 = 162 + -162 Combine like terms: 162 + -162 = 0 -162 + 12x + 2.5x2 = 0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -64.8 + 4.8x + x2 = 0 Move the constant term to the right: Add '64.8' to each side of the equation. -64.8 + 4.8x + 64.8 + x2 = 0 + 64.8 Reorder the terms: -64.8 + 64.8 + 4.8x + x2 = 0 + 64.8 Combine like terms: -64.8 + 64.8 = 0.0 0.0 + 4.8x + x2 = 0 + 64.8 4.8x + x2 = 0 + 64.8 Combine like terms: 0 + 64.8 = 64.8 4.8x + x2 = 64.8 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 = 64.8 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 64.8 + 5.76 Combine like terms: 64.8 + 5.76 = 70.56 5.76 + 4.8x + x2 = 70.56 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 70.56 Calculate the square root of the right side: 8.4 Break this problem into two subproblems by setting (x + 2.4) equal to 8.4 and -8.4.Subproblem 1
x + 2.4 = 8.4 Simplifying x + 2.4 = 8.4 Reorder the terms: 2.4 + x = 8.4 Solving 2.4 + x = 8.4 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 = 8.4 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 8.4 + -2.4 x = 8.4 + -2.4 Combine like terms: 8.4 + -2.4 = 6 x = 6 Simplifying x = 6Subproblem 2
x + 2.4 = -8.4 Simplifying x + 2.4 = -8.4 Reorder the terms: 2.4 + x = -8.4 Solving 2.4 + x = -8.4 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 = -8.4 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -8.4 + -2.4 x = -8.4 + -2.4 Combine like terms: -8.4 + -2.4 = -10.8 x = -10.8 Simplifying x = -10.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, -10.8}
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