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Simplifying x2 + -30.8x + 78.4 = 0 Reorder the terms: 78.4 + -30.8x + x2 = 0 Solving 78.4 + -30.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-78.4' to each side of the equation. 78.4 + -30.8x + -78.4 + x2 = 0 + -78.4 Reorder the terms: 78.4 + -78.4 + -30.8x + x2 = 0 + -78.4 Combine like terms: 78.4 + -78.4 = 0.0 0.0 + -30.8x + x2 = 0 + -78.4 -30.8x + x2 = 0 + -78.4 Combine like terms: 0 + -78.4 = -78.4 -30.8x + x2 = -78.4 The x term is -30.8x. Take half its coefficient (-15.4). Square it (237.16) and add it to both sides. Add '237.16' to each side of the equation. -30.8x + 237.16 + x2 = -78.4 + 237.16 Reorder the terms: 237.16 + -30.8x + x2 = -78.4 + 237.16 Combine like terms: -78.4 + 237.16 = 158.76 237.16 + -30.8x + x2 = 158.76 Factor a perfect square on the left side: (x + -15.4)(x + -15.4) = 158.76 Calculate the square root of the right side: 12.6 Break this problem into two subproblems by setting (x + -15.4) equal to 12.6 and -12.6.Subproblem 1
x + -15.4 = 12.6 Simplifying x + -15.4 = 12.6 Reorder the terms: -15.4 + x = 12.6 Solving -15.4 + x = 12.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.4' to each side of the equation. -15.4 + 15.4 + x = 12.6 + 15.4 Combine like terms: -15.4 + 15.4 = 0.0 0.0 + x = 12.6 + 15.4 x = 12.6 + 15.4 Combine like terms: 12.6 + 15.4 = 28 x = 28 Simplifying x = 28Subproblem 2
x + -15.4 = -12.6 Simplifying x + -15.4 = -12.6 Reorder the terms: -15.4 + x = -12.6 Solving -15.4 + x = -12.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.4' to each side of the equation. -15.4 + 15.4 + x = -12.6 + 15.4 Combine like terms: -15.4 + 15.4 = 0.0 0.0 + x = -12.6 + 15.4 x = -12.6 + 15.4 Combine like terms: -12.6 + 15.4 = 2.8 x = 2.8 Simplifying x = 2.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {28, 2.8}
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