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Simplifying x2 + 6x = 630 Reorder the terms: 6x + x2 = 630 Solving 6x + x2 = 630 Solving for variable 'x'. Reorder the terms: -630 + 6x + x2 = 630 + -630 Combine like terms: 630 + -630 = 0 -630 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '630' to each side of the equation. -630 + 6x + 630 + x2 = 0 + 630 Reorder the terms: -630 + 630 + 6x + x2 = 0 + 630 Combine like terms: -630 + 630 = 0 0 + 6x + x2 = 0 + 630 6x + x2 = 0 + 630 Combine like terms: 0 + 630 = 630 6x + x2 = 630 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 = 630 + 9 Reorder the terms: 9 + 6x + x2 = 630 + 9 Combine like terms: 630 + 9 = 639 9 + 6x + x2 = 639 Factor a perfect square on the left side: (x + 3)(x + 3) = 639 Calculate the square root of the right side: 25.27844932 Break this problem into two subproblems by setting (x + 3) equal to 25.27844932 and -25.27844932.Subproblem 1
x + 3 = 25.27844932 Simplifying x + 3 = 25.27844932 Reorder the terms: 3 + x = 25.27844932 Solving 3 + x = 25.27844932 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 = 25.27844932 + -3 Combine like terms: 3 + -3 = 0 0 + x = 25.27844932 + -3 x = 25.27844932 + -3 Combine like terms: 25.27844932 + -3 = 22.27844932 x = 22.27844932 Simplifying x = 22.27844932Subproblem 2
x + 3 = -25.27844932 Simplifying x + 3 = -25.27844932 Reorder the terms: 3 + x = -25.27844932 Solving 3 + x = -25.27844932 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 = -25.27844932 + -3 Combine like terms: 3 + -3 = 0 0 + x = -25.27844932 + -3 x = -25.27844932 + -3 Combine like terms: -25.27844932 + -3 = -28.27844932 x = -28.27844932 Simplifying x = -28.27844932Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.27844932, -28.27844932}
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