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Simplifying 5x2 + -445 = -30x Reorder the terms: -445 + 5x2 = -30x Solving -445 + 5x2 = -30x Solving for variable 'x'. Reorder the terms: -445 + 30x + 5x2 = -30x + 30x Combine like terms: -30x + 30x = 0 -445 + 30x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-89 + 6x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-89 + 6x + x2)' equal to zero and attempt to solve: Simplifying -89 + 6x + x2 = 0 Solving -89 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 6x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + 6x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 6x + x2 = 0 + 89 6x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 6x + x2 = 89 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 89 + 9 Reorder the terms: 9 + 6x + x2 = 89 + 9 Combine like terms: 89 + 9 = 98 9 + 6x + x2 = 98 Factor a perfect square on the left side: (x + 3)(x + 3) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + 3) equal to 9.899494937 and -9.899494937.Subproblem 1
x + 3 = 9.899494937 Simplifying x + 3 = 9.899494937 Reorder the terms: 3 + x = 9.899494937 Solving 3 + x = 9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 9.899494937 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.899494937 + -3 x = 9.899494937 + -3 Combine like terms: 9.899494937 + -3 = 6.899494937 x = 6.899494937 Simplifying x = 6.899494937Subproblem 2
x + 3 = -9.899494937 Simplifying x + 3 = -9.899494937 Reorder the terms: 3 + x = -9.899494937 Solving 3 + x = -9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -9.899494937 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.899494937 + -3 x = -9.899494937 + -3 Combine like terms: -9.899494937 + -3 = -12.899494937 x = -12.899494937 Simplifying x = -12.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.899494937, -12.899494937}Solution
x = {6.899494937, -12.899494937}
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