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Simplifying (x + 30) * 5x + 3 = 1770 Reorder the terms: (30 + x) * 5x + 3 = 1770 Reorder the terms for easier multiplication: 5x(30 + x) + 3 = 1770 (30 * 5x + x * 5x) + 3 = 1770 (150x + 5x2) + 3 = 1770 Reorder the terms: 3 + 150x + 5x2 = 1770 Solving 3 + 150x + 5x2 = 1770 Solving for variable 'x'. Reorder the terms: 3 + -1770 + 150x + 5x2 = 1770 + -1770 Combine like terms: 3 + -1770 = -1767 -1767 + 150x + 5x2 = 1770 + -1770 Combine like terms: 1770 + -1770 = 0 -1767 + 150x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -353.4 + 30x + x2 = 0 Move the constant term to the right: Add '353.4' to each side of the equation. -353.4 + 30x + 353.4 + x2 = 0 + 353.4 Reorder the terms: -353.4 + 353.4 + 30x + x2 = 0 + 353.4 Combine like terms: -353.4 + 353.4 = 0.0 0.0 + 30x + x2 = 0 + 353.4 30x + x2 = 0 + 353.4 Combine like terms: 0 + 353.4 = 353.4 30x + x2 = 353.4 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 = 353.4 + 225 Reorder the terms: 225 + 30x + x2 = 353.4 + 225 Combine like terms: 353.4 + 225 = 578.4 225 + 30x + x2 = 578.4 Factor a perfect square on the left side: (x + 15)(x + 15) = 578.4 Calculate the square root of the right side: 24.049948025 Break this problem into two subproblems by setting (x + 15) equal to 24.049948025 and -24.049948025.Subproblem 1
x + 15 = 24.049948025 Simplifying x + 15 = 24.049948025 Reorder the terms: 15 + x = 24.049948025 Solving 15 + x = 24.049948025 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 = 24.049948025 + -15 Combine like terms: 15 + -15 = 0 0 + x = 24.049948025 + -15 x = 24.049948025 + -15 Combine like terms: 24.049948025 + -15 = 9.049948025 x = 9.049948025 Simplifying x = 9.049948025Subproblem 2
x + 15 = -24.049948025 Simplifying x + 15 = -24.049948025 Reorder the terms: 15 + x = -24.049948025 Solving 15 + x = -24.049948025 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 = -24.049948025 + -15 Combine like terms: 15 + -15 = 0 0 + x = -24.049948025 + -15 x = -24.049948025 + -15 Combine like terms: -24.049948025 + -15 = -39.049948025 x = -39.049948025 Simplifying x = -39.049948025Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.049948025, -39.049948025}
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