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Simplifying 0.3x + -1 = 1x(x + 30) Reorder the terms: -1 + 0.3x = 1x(x + 30) Reorder the terms: -1 + 0.3x = 1x(30 + x) -1 + 0.3x = (30 * 1x + x * 1x) -1 + 0.3x = (30x + 1x2) Solving -1 + 0.3x = 30x + 1x2 Solving for variable 'x'. Combine like terms: 0.3x + -30x = -29.7x -1 + -29.7x + -1x2 = 30x + 1x2 + -30x + -1x2 Reorder the terms: -1 + -29.7x + -1x2 = 30x + -30x + 1x2 + -1x2 Combine like terms: 30x + -30x = 0 -1 + -29.7x + -1x2 = 0 + 1x2 + -1x2 -1 + -29.7x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -1 + -29.7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + 29.7x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 29.7x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 29.7x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 29.7x + x2 = 0 + -1 29.7x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 29.7x + x2 = -1 The x term is 29.7x. Take half its coefficient (14.85). Square it (220.5225) and add it to both sides. Add '220.5225' to each side of the equation. 29.7x + 220.5225 + x2 = -1 + 220.5225 Reorder the terms: 220.5225 + 29.7x + x2 = -1 + 220.5225 Combine like terms: -1 + 220.5225 = 219.5225 220.5225 + 29.7x + x2 = 219.5225 Factor a perfect square on the left side: (x + 14.85)(x + 14.85) = 219.5225 Calculate the square root of the right side: 14.816291709 Break this problem into two subproblems by setting (x + 14.85) equal to 14.816291709 and -14.816291709.Subproblem 1
x + 14.85 = 14.816291709 Simplifying x + 14.85 = 14.816291709 Reorder the terms: 14.85 + x = 14.816291709 Solving 14.85 + x = 14.816291709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.85' to each side of the equation. 14.85 + -14.85 + x = 14.816291709 + -14.85 Combine like terms: 14.85 + -14.85 = 0.00 0.00 + x = 14.816291709 + -14.85 x = 14.816291709 + -14.85 Combine like terms: 14.816291709 + -14.85 = -0.033708291 x = -0.033708291 Simplifying x = -0.033708291Subproblem 2
x + 14.85 = -14.816291709 Simplifying x + 14.85 = -14.816291709 Reorder the terms: 14.85 + x = -14.816291709 Solving 14.85 + x = -14.816291709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.85' to each side of the equation. 14.85 + -14.85 + x = -14.816291709 + -14.85 Combine like terms: 14.85 + -14.85 = 0.00 0.00 + x = -14.816291709 + -14.85 x = -14.816291709 + -14.85 Combine like terms: -14.816291709 + -14.85 = -29.666291709 x = -29.666291709 Simplifying x = -29.666291709Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.033708291, -29.666291709}
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