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Simplifying x2 + 14x + 45 = -6x + 30 Reorder the terms: 45 + 14x + x2 = -6x + 30 Reorder the terms: 45 + 14x + x2 = 30 + -6x Solving 45 + 14x + x2 = 30 + -6x Solving for variable 'x'. Reorder the terms: 45 + -30 + 14x + 6x + x2 = 30 + -6x + -30 + 6x Combine like terms: 45 + -30 = 15 15 + 14x + 6x + x2 = 30 + -6x + -30 + 6x Combine like terms: 14x + 6x = 20x 15 + 20x + x2 = 30 + -6x + -30 + 6x Reorder the terms: 15 + 20x + x2 = 30 + -30 + -6x + 6x Combine like terms: 30 + -30 = 0 15 + 20x + x2 = 0 + -6x + 6x 15 + 20x + x2 = -6x + 6x Combine like terms: -6x + 6x = 0 15 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 20x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 20x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 20x + x2 = 0 + -15 20x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 20x + x2 = -15 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -15 + 100 Reorder the terms: 100 + 20x + x2 = -15 + 100 Combine like terms: -15 + 100 = 85 100 + 20x + x2 = 85 Factor a perfect square on the left side: (x + 10)(x + 10) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + 10) equal to 9.219544457 and -9.219544457.Subproblem 1
x + 10 = 9.219544457 Simplifying x + 10 = 9.219544457 Reorder the terms: 10 + x = 9.219544457 Solving 10 + x = 9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 9.219544457 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.219544457 + -10 x = 9.219544457 + -10 Combine like terms: 9.219544457 + -10 = -0.780455543 x = -0.780455543 Simplifying x = -0.780455543Subproblem 2
x + 10 = -9.219544457 Simplifying x + 10 = -9.219544457 Reorder the terms: 10 + x = -9.219544457 Solving 10 + x = -9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -9.219544457 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.219544457 + -10 x = -9.219544457 + -10 Combine like terms: -9.219544457 + -10 = -19.219544457 x = -19.219544457 Simplifying x = -19.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.780455543, -19.219544457}
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