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Simplifying x(5x + 1) = 21x + 45 Reorder the terms: x(1 + 5x) = 21x + 45 (1 * x + 5x * x) = 21x + 45 (1x + 5x2) = 21x + 45 Reorder the terms: 1x + 5x2 = 45 + 21x Solving 1x + 5x2 = 45 + 21x Solving for variable 'x'. Reorder the terms: -45 + 1x + -21x + 5x2 = 45 + 21x + -45 + -21x Combine like terms: 1x + -21x = -20x -45 + -20x + 5x2 = 45 + 21x + -45 + -21x Reorder the terms: -45 + -20x + 5x2 = 45 + -45 + 21x + -21x Combine like terms: 45 + -45 = 0 -45 + -20x + 5x2 = 0 + 21x + -21x -45 + -20x + 5x2 = 21x + -21x Combine like terms: 21x + -21x = 0 -45 + -20x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + -4x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + -4x + x2)' equal to zero and attempt to solve: Simplifying -9 + -4x + x2 = 0 Solving -9 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -4x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -4x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4x + x2 = 0 + 9 -4x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -4x + x2 = 9 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 9 + 4 Reorder the terms: 4 + -4x + x2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + -4x + x2 = 13 Factor a perfect square on the left side: (x + -2)(x + -2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -2) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -2 = 3.605551275 Simplifying x + -2 = 3.605551275 Reorder the terms: -2 + x = 3.605551275 Solving -2 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.605551275 + 2 x = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 x = 5.605551275 Simplifying x = 5.605551275Subproblem 2
x + -2 = -3.605551275 Simplifying x + -2 = -3.605551275 Reorder the terms: -2 + x = -3.605551275 Solving -2 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.605551275 + 2 x = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 x = -1.605551275 Simplifying x = -1.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.605551275, -1.605551275}Solution
x = {5.605551275, -1.605551275}
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