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Simplifying -1(x2 + 12x + 36) + -2 + (x2 + 10x + 25) + -1x2 + -8x + 16 = 0 Reorder the terms: -1(36 + 12x + x2) + -2 + (x2 + 10x + 25) + -1x2 + -8x + 16 = 0 (36 * -1 + 12x * -1 + x2 * -1) + -2 + (x2 + 10x + 25) + -1x2 + -8x + 16 = 0 (-36 + -12x + -1x2) + -2 + (x2 + 10x + 25) + -1x2 + -8x + 16 = 0 Reorder the terms: -36 + -12x + -1x2 + -2 + (25 + 10x + x2) + -1x2 + -8x + 16 = 0 Remove parenthesis around (25 + 10x + x2) -36 + -12x + -1x2 + -2 + 25 + 10x + x2 + -1x2 + -8x + 16 = 0 Reorder the terms: -36 + -2 + 25 + 16 + -12x + 10x + -8x + -1x2 + x2 + -1x2 = 0 Combine like terms: -36 + -2 = -38 -38 + 25 + 16 + -12x + 10x + -8x + -1x2 + x2 + -1x2 = 0 Combine like terms: -38 + 25 = -13 -13 + 16 + -12x + 10x + -8x + -1x2 + x2 + -1x2 = 0 Combine like terms: -13 + 16 = 3 3 + -12x + 10x + -8x + -1x2 + x2 + -1x2 = 0 Combine like terms: -12x + 10x = -2x 3 + -2x + -8x + -1x2 + x2 + -1x2 = 0 Combine like terms: -2x + -8x = -10x 3 + -10x + -1x2 + x2 + -1x2 = 0 Combine like terms: -1x2 + x2 = 0 3 + -10x + 0 + -1x2 = 0 3 + -10x + -1x2 = 0 Solving 3 + -10x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 10x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 10x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 10x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 10x + x2 = 0 + 3 10x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 10x + x2 = 3 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 3 + 25 Reorder the terms: 25 + 10x + x2 = 3 + 25 Combine like terms: 3 + 25 = 28 25 + 10x + x2 = 28 Factor a perfect square on the left side: (x + 5)(x + 5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 5) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 5 = 5.291502622 Simplifying x + 5 = 5.291502622 Reorder the terms: 5 + x = 5.291502622 Solving 5 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.291502622 + -5 x = 5.291502622 + -5 Combine like terms: 5.291502622 + -5 = 0.291502622 x = 0.291502622 Simplifying x = 0.291502622Subproblem 2
x + 5 = -5.291502622 Simplifying x + 5 = -5.291502622 Reorder the terms: 5 + x = -5.291502622 Solving 5 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.291502622 + -5 x = -5.291502622 + -5 Combine like terms: -5.291502622 + -5 = -10.291502622 x = -10.291502622 Simplifying x = -10.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.291502622, -10.291502622}
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