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Simplifying x2 + -19.8x + 32.4 = 0 Reorder the terms: 32.4 + -19.8x + x2 = 0 Solving 32.4 + -19.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-32.4' to each side of the equation. 32.4 + -19.8x + -32.4 + x2 = 0 + -32.4 Reorder the terms: 32.4 + -32.4 + -19.8x + x2 = 0 + -32.4 Combine like terms: 32.4 + -32.4 = 0.0 0.0 + -19.8x + x2 = 0 + -32.4 -19.8x + x2 = 0 + -32.4 Combine like terms: 0 + -32.4 = -32.4 -19.8x + x2 = -32.4 The x term is -19.8x. Take half its coefficient (-9.9). Square it (98.01) and add it to both sides. Add '98.01' to each side of the equation. -19.8x + 98.01 + x2 = -32.4 + 98.01 Reorder the terms: 98.01 + -19.8x + x2 = -32.4 + 98.01 Combine like terms: -32.4 + 98.01 = 65.61 98.01 + -19.8x + x2 = 65.61 Factor a perfect square on the left side: (x + -9.9)(x + -9.9) = 65.61 Calculate the square root of the right side: 8.1 Break this problem into two subproblems by setting (x + -9.9) equal to 8.1 and -8.1.Subproblem 1
x + -9.9 = 8.1 Simplifying x + -9.9 = 8.1 Reorder the terms: -9.9 + x = 8.1 Solving -9.9 + x = 8.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.9' to each side of the equation. -9.9 + 9.9 + x = 8.1 + 9.9 Combine like terms: -9.9 + 9.9 = 0.0 0.0 + x = 8.1 + 9.9 x = 8.1 + 9.9 Combine like terms: 8.1 + 9.9 = 18 x = 18 Simplifying x = 18Subproblem 2
x + -9.9 = -8.1 Simplifying x + -9.9 = -8.1 Reorder the terms: -9.9 + x = -8.1 Solving -9.9 + x = -8.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.9' to each side of the equation. -9.9 + 9.9 + x = -8.1 + 9.9 Combine like terms: -9.9 + 9.9 = 0.0 0.0 + x = -8.1 + 9.9 x = -8.1 + 9.9 Combine like terms: -8.1 + 9.9 = 1.8 x = 1.8 Simplifying x = 1.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {18, 1.8}
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