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Simplifying x + x(x + 45) + (x + 45) + (x + 45) = 0 Reorder the terms: x + x(45 + x) + (x + 45) + (x + 45) = 0 x + (45 * x + x * x) + (x + 45) + (x + 45) = 0 x + (45x + x2) + (x + 45) + (x + 45) = 0 Reorder the terms: x + 45x + x2 + (45 + x) + (x + 45) = 0 Remove parenthesis around (45 + x) x + 45x + x2 + 45 + x + (x + 45) = 0 Reorder the terms: x + 45x + x2 + 45 + x + (45 + x) = 0 Remove parenthesis around (45 + x) x + 45x + x2 + 45 + x + 45 + x = 0 Reorder the terms: 45 + 45 + x + 45x + x + x + x2 = 0 Combine like terms: 45 + 45 = 90 90 + x + 45x + x + x + x2 = 0 Combine like terms: x + 45x = 46x 90 + 46x + x + x + x2 = 0 Combine like terms: 46x + x = 47x 90 + 47x + x + x2 = 0 Combine like terms: 47x + x = 48x 90 + 48x + x2 = 0 Solving 90 + 48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + 48x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + 48x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + 48x + x2 = 0 + -90 48x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 48x + x2 = -90 The x term is 48x. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48x + 576 + x2 = -90 + 576 Reorder the terms: 576 + 48x + x2 = -90 + 576 Combine like terms: -90 + 576 = 486 576 + 48x + x2 = 486 Factor a perfect square on the left side: (x + 24)(x + 24) = 486 Calculate the square root of the right side: 22.045407685 Break this problem into two subproblems by setting (x + 24) equal to 22.045407685 and -22.045407685.Subproblem 1
x + 24 = 22.045407685 Simplifying x + 24 = 22.045407685 Reorder the terms: 24 + x = 22.045407685 Solving 24 + x = 22.045407685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 22.045407685 + -24 Combine like terms: 24 + -24 = 0 0 + x = 22.045407685 + -24 x = 22.045407685 + -24 Combine like terms: 22.045407685 + -24 = -1.954592315 x = -1.954592315 Simplifying x = -1.954592315Subproblem 2
x + 24 = -22.045407685 Simplifying x + 24 = -22.045407685 Reorder the terms: 24 + x = -22.045407685 Solving 24 + x = -22.045407685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = -22.045407685 + -24 Combine like terms: 24 + -24 = 0 0 + x = -22.045407685 + -24 x = -22.045407685 + -24 Combine like terms: -22.045407685 + -24 = -46.045407685 x = -46.045407685 Simplifying x = -46.045407685Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.954592315, -46.045407685}
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