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Simplifying 0 = x2 + -30x + 80 Reorder the terms: 0 = 80 + -30x + x2 Solving 0 = 80 + -30x + x2 Solving for variable 'x'. Combine like terms: 0 + -80 = -80 -80 + 30x + -1x2 = 80 + -30x + x2 + -80 + 30x + -1x2 Reorder the terms: -80 + 30x + -1x2 = 80 + -80 + -30x + 30x + x2 + -1x2 Combine like terms: 80 + -80 = 0 -80 + 30x + -1x2 = 0 + -30x + 30x + x2 + -1x2 -80 + 30x + -1x2 = -30x + 30x + x2 + -1x2 Combine like terms: -30x + 30x = 0 -80 + 30x + -1x2 = 0 + x2 + -1x2 -80 + 30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -80 + 30x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 80 + -30x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -30x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -30x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -30x + x2 = 0 + -80 -30x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -30x + x2 = -80 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -80 + 225 Reorder the terms: 225 + -30x + x2 = -80 + 225 Combine like terms: -80 + 225 = 145 225 + -30x + x2 = 145 Factor a perfect square on the left side: (x + -15)(x + -15) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + -15) equal to 12.041594579 and -12.041594579.Subproblem 1
x + -15 = 12.041594579 Simplifying x + -15 = 12.041594579 Reorder the terms: -15 + x = 12.041594579 Solving -15 + x = 12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 12.041594579 + 15 Combine like terms: -15 + 15 = 0 0 + x = 12.041594579 + 15 x = 12.041594579 + 15 Combine like terms: 12.041594579 + 15 = 27.041594579 x = 27.041594579 Simplifying x = 27.041594579Subproblem 2
x + -15 = -12.041594579 Simplifying x + -15 = -12.041594579 Reorder the terms: -15 + x = -12.041594579 Solving -15 + x = -12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -12.041594579 + 15 Combine like terms: -15 + 15 = 0 0 + x = -12.041594579 + 15 x = -12.041594579 + 15 Combine like terms: -12.041594579 + 15 = 2.958405421 x = 2.958405421 Simplifying x = 2.958405421Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.041594579, 2.958405421}
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