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Simplifying 0.2 = (x + -30) * x Reorder the terms: 0.2 = (-30 + x) * x Reorder the terms for easier multiplication: 0.2 = x(-30 + x) 0.2 = (-30 * x + x * x) 0.2 = (-30x + x2) Solving 0.2 = -30x + x2 Solving for variable 'x'. Reorder the terms: 0.2 + 30x + -1x2 = -30x + 30x + x2 + -1x2 Combine like terms: -30x + 30x = 0 0.2 + 30x + -1x2 = 0 + x2 + -1x2 0.2 + 30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.2 + 30x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.2 + -30x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -30x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -30x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -30x + x2 = 0 + 0.2 -30x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -30x + x2 = 0.2 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 = 0.2 + 225 Reorder the terms: 225 + -30x + x2 = 0.2 + 225 Combine like terms: 0.2 + 225 = 225.2 225 + -30x + x2 = 225.2 Factor a perfect square on the left side: (x + -15)(x + -15) = 225.2 Calculate the square root of the right side: 15.006665186 Break this problem into two subproblems by setting (x + -15) equal to 15.006665186 and -15.006665186.Subproblem 1
x + -15 = 15.006665186 Simplifying x + -15 = 15.006665186 Reorder the terms: -15 + x = 15.006665186 Solving -15 + x = 15.006665186 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 = 15.006665186 + 15 Combine like terms: -15 + 15 = 0 0 + x = 15.006665186 + 15 x = 15.006665186 + 15 Combine like terms: 15.006665186 + 15 = 30.006665186 x = 30.006665186 Simplifying x = 30.006665186Subproblem 2
x + -15 = -15.006665186 Simplifying x + -15 = -15.006665186 Reorder the terms: -15 + x = -15.006665186 Solving -15 + x = -15.006665186 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 = -15.006665186 + 15 Combine like terms: -15 + 15 = 0 0 + x = -15.006665186 + 15 x = -15.006665186 + 15 Combine like terms: -15.006665186 + 15 = -0.006665186 x = -0.006665186 Simplifying x = -0.006665186Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.006665186, -0.006665186}
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