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Simplifying 4x + 800 = x2 + 10x Reorder the terms: 800 + 4x = x2 + 10x Reorder the terms: 800 + 4x = 10x + x2 Solving 800 + 4x = 10x + x2 Solving for variable 'x'. Combine like terms: 4x + -10x = -6x 800 + -6x + -1x2 = 10x + x2 + -10x + -1x2 Reorder the terms: 800 + -6x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 800 + -6x + -1x2 = 0 + x2 + -1x2 800 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 800 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -800 + 6x + x2 = 0 Move the constant term to the right: Add '800' to each side of the equation. -800 + 6x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + 6x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 6x + x2 = 0 + 800 6x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 6x + x2 = 800 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 = 800 + 9 Reorder the terms: 9 + 6x + x2 = 800 + 9 Combine like terms: 800 + 9 = 809 9 + 6x + x2 = 809 Factor a perfect square on the left side: (x + 3)(x + 3) = 809 Calculate the square root of the right side: 28.442925307 Break this problem into two subproblems by setting (x + 3) equal to 28.442925307 and -28.442925307.Subproblem 1
x + 3 = 28.442925307 Simplifying x + 3 = 28.442925307 Reorder the terms: 3 + x = 28.442925307 Solving 3 + x = 28.442925307 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 = 28.442925307 + -3 Combine like terms: 3 + -3 = 0 0 + x = 28.442925307 + -3 x = 28.442925307 + -3 Combine like terms: 28.442925307 + -3 = 25.442925307 x = 25.442925307 Simplifying x = 25.442925307Subproblem 2
x + 3 = -28.442925307 Simplifying x + 3 = -28.442925307 Reorder the terms: 3 + x = -28.442925307 Solving 3 + x = -28.442925307 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 = -28.442925307 + -3 Combine like terms: 3 + -3 = 0 0 + x = -28.442925307 + -3 x = -28.442925307 + -3 Combine like terms: -28.442925307 + -3 = -31.442925307 x = -31.442925307 Simplifying x = -31.442925307Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.442925307, -31.442925307}
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