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Simplifying 20 + -5x + -1(x2 + 8x + -16) + 7 = 0 Reorder the terms: 20 + -5x + -1(-16 + 8x + x2) + 7 = 0 20 + -5x + (-16 * -1 + 8x * -1 + x2 * -1) + 7 = 0 20 + -5x + (16 + -8x + -1x2) + 7 = 0 Reorder the terms: 20 + 16 + 7 + -5x + -8x + -1x2 = 0 Combine like terms: 20 + 16 = 36 36 + 7 + -5x + -8x + -1x2 = 0 Combine like terms: 36 + 7 = 43 43 + -5x + -8x + -1x2 = 0 Combine like terms: -5x + -8x = -13x 43 + -13x + -1x2 = 0 Solving 43 + -13x + -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'. -43 + 13x + x2 = 0 Move the constant term to the right: Add '43' to each side of the equation. -43 + 13x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + 13x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 13x + x2 = 0 + 43 13x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 13x + x2 = 43 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 43 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 43 + 42.25 Combine like terms: 43 + 42.25 = 85.25 42.25 + 13x + x2 = 85.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x + 6.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x + 6.5 = 9.233092656 Simplifying x + 6.5 = 9.233092656 Reorder the terms: 6.5 + x = 9.233092656 Solving 6.5 + x = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 9.233092656 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 9.233092656 + -6.5 x = 9.233092656 + -6.5 Combine like terms: 9.233092656 + -6.5 = 2.733092656 x = 2.733092656 Simplifying x = 2.733092656Subproblem 2
x + 6.5 = -9.233092656 Simplifying x + 6.5 = -9.233092656 Reorder the terms: 6.5 + x = -9.233092656 Solving 6.5 + x = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -9.233092656 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -9.233092656 + -6.5 x = -9.233092656 + -6.5 Combine like terms: -9.233092656 + -6.5 = -15.733092656 x = -15.733092656 Simplifying x = -15.733092656Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.733092656, -15.733092656}
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