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Simplifying 0.1x * x + -3x = 9.9 Multiply x * x 0.1x2 + -3x = 9.9 Reorder the terms: -3x + 0.1x2 = 9.9 Solving -3x + 0.1x2 = 9.9 Solving for variable 'x'. Reorder the terms: -9.9 + -3x + 0.1x2 = 9.9 + -9.9 Combine like terms: 9.9 + -9.9 = 0.0 -9.9 + -3x + 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'. -99 + -30x + x2 = 0 Move the constant term to the right: Add '99' to each side of the equation. -99 + -30x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -30x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -30x + x2 = 0 + 99 -30x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -30x + x2 = 99 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 = 99 + 225 Reorder the terms: 225 + -30x + x2 = 99 + 225 Combine like terms: 99 + 225 = 324 225 + -30x + x2 = 324 Factor a perfect square on the left side: (x + -15)(x + -15) = 324 Calculate the square root of the right side: 18 Break this problem into two subproblems by setting (x + -15) equal to 18 and -18.Subproblem 1
x + -15 = 18 Simplifying x + -15 = 18 Reorder the terms: -15 + x = 18 Solving -15 + x = 18 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 = 18 + 15 Combine like terms: -15 + 15 = 0 0 + x = 18 + 15 x = 18 + 15 Combine like terms: 18 + 15 = 33 x = 33 Simplifying x = 33Subproblem 2
x + -15 = -18 Simplifying x + -15 = -18 Reorder the terms: -15 + x = -18 Solving -15 + x = -18 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 = -18 + 15 Combine like terms: -15 + 15 = 0 0 + x = -18 + 15 x = -18 + 15 Combine like terms: -18 + 15 = -3 x = -3 Simplifying x = -3Solution
The solution to the problem is based on the solutions from the subproblems. x = {33, -3}
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