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Simplifying 14x + -0.2x2 = 30 Solving 14x + -0.2x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 14x + -0.2x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 14x + -0.2x2 = 0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 150 + -70x + x2 = 0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + -70x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -70x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -70x + x2 = 0 + -150 -70x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -70x + x2 = -150 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = -150 + 1225 Reorder the terms: 1225 + -70x + x2 = -150 + 1225 Combine like terms: -150 + 1225 = 1075 1225 + -70x + x2 = 1075 Factor a perfect square on the left side: (x + -35)(x + -35) = 1075 Calculate the square root of the right side: 32.787192622 Break this problem into two subproblems by setting (x + -35) equal to 32.787192622 and -32.787192622.Subproblem 1
x + -35 = 32.787192622 Simplifying x + -35 = 32.787192622 Reorder the terms: -35 + x = 32.787192622 Solving -35 + x = 32.787192622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 32.787192622 + 35 Combine like terms: -35 + 35 = 0 0 + x = 32.787192622 + 35 x = 32.787192622 + 35 Combine like terms: 32.787192622 + 35 = 67.787192622 x = 67.787192622 Simplifying x = 67.787192622Subproblem 2
x + -35 = -32.787192622 Simplifying x + -35 = -32.787192622 Reorder the terms: -35 + x = -32.787192622 Solving -35 + x = -32.787192622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -32.787192622 + 35 Combine like terms: -35 + 35 = 0 0 + x = -32.787192622 + 35 x = -32.787192622 + 35 Combine like terms: -32.787192622 + 35 = 2.212807378 x = 2.212807378 Simplifying x = 2.212807378Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.787192622, 2.212807378}
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