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Simplifying 0 = -0.1x2 + 4x + -10 Reorder the terms: 0 = -10 + 4x + -0.1x2 Solving 0 = -10 + 4x + -0.1x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -4x + 0.1x2 = -10 + 4x + -0.1x2 + 10 + -4x + 0.1x2 Reorder the terms: 10 + -4x + 0.1x2 = -10 + 10 + 4x + -4x + -0.1x2 + 0.1x2 Combine like terms: -10 + 10 = 0 10 + -4x + 0.1x2 = 0 + 4x + -4x + -0.1x2 + 0.1x2 10 + -4x + 0.1x2 = 4x + -4x + -0.1x2 + 0.1x2 Combine like terms: 4x + -4x = 0 10 + -4x + 0.1x2 = 0 + -0.1x2 + 0.1x2 10 + -4x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 10 + -4x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 100 + -40x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -40x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -40x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -40x + x2 = 0 + -100 -40x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -40x + x2 = -100 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -100 + 400 Reorder the terms: 400 + -40x + x2 = -100 + 400 Combine like terms: -100 + 400 = 300 400 + -40x + x2 = 300 Factor a perfect square on the left side: (x + -20)(x + -20) = 300 Calculate the square root of the right side: 17.320508076 Break this problem into two subproblems by setting (x + -20) equal to 17.320508076 and -17.320508076.Subproblem 1
x + -20 = 17.320508076 Simplifying x + -20 = 17.320508076 Reorder the terms: -20 + x = 17.320508076 Solving -20 + x = 17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 17.320508076 + 20 Combine like terms: -20 + 20 = 0 0 + x = 17.320508076 + 20 x = 17.320508076 + 20 Combine like terms: 17.320508076 + 20 = 37.320508076 x = 37.320508076 Simplifying x = 37.320508076Subproblem 2
x + -20 = -17.320508076 Simplifying x + -20 = -17.320508076 Reorder the terms: -20 + x = -17.320508076 Solving -20 + x = -17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -17.320508076 + 20 Combine like terms: -20 + 20 = 0 0 + x = -17.320508076 + 20 x = -17.320508076 + 20 Combine like terms: -17.320508076 + 20 = 2.679491924 x = 2.679491924 Simplifying x = 2.679491924Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.320508076, 2.679491924}
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