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Simplifying 0.1x2 + 3x + 20 = 36 Reorder the terms: 20 + 3x + 0.1x2 = 36 Solving 20 + 3x + 0.1x2 = 36 Solving for variable 'x'. Reorder the terms: 20 + -36 + 3x + 0.1x2 = 36 + -36 Combine like terms: 20 + -36 = -16 -16 + 3x + 0.1x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -16 + 3x + 0.1x2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -160 + 30x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + 30x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 30x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 30x + x2 = 0 + 160 30x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 30x + x2 = 160 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 = 160 + 225 Reorder the terms: 225 + 30x + x2 = 160 + 225 Combine like terms: 160 + 225 = 385 225 + 30x + x2 = 385 Factor a perfect square on the left side: (x + 15)(x + 15) = 385 Calculate the square root of the right side: 19.62141687 Break this problem into two subproblems by setting (x + 15) equal to 19.62141687 and -19.62141687.Subproblem 1
x + 15 = 19.62141687 Simplifying x + 15 = 19.62141687 Reorder the terms: 15 + x = 19.62141687 Solving 15 + x = 19.62141687 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 = 19.62141687 + -15 Combine like terms: 15 + -15 = 0 0 + x = 19.62141687 + -15 x = 19.62141687 + -15 Combine like terms: 19.62141687 + -15 = 4.62141687 x = 4.62141687 Simplifying x = 4.62141687Subproblem 2
x + 15 = -19.62141687 Simplifying x + 15 = -19.62141687 Reorder the terms: 15 + x = -19.62141687 Solving 15 + x = -19.62141687 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 = -19.62141687 + -15 Combine like terms: 15 + -15 = 0 0 + x = -19.62141687 + -15 x = -19.62141687 + -15 Combine like terms: -19.62141687 + -15 = -34.62141687 x = -34.62141687 Simplifying x = -34.62141687Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.62141687, -34.62141687}
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