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Simplifying x2 + -12x + -20 = 9 Reorder the terms: -20 + -12x + x2 = 9 Solving -20 + -12x + x2 = 9 Solving for variable 'x'. Reorder the terms: -20 + -9 + -12x + x2 = 9 + -9 Combine like terms: -20 + -9 = -29 -29 + -12x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -29 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -12x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -12x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -12x + x2 = 0 + 29 -12x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -12x + x2 = 29 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 29 + 36 Reorder the terms: 36 + -12x + x2 = 29 + 36 Combine like terms: 29 + 36 = 65 36 + -12x + x2 = 65 Factor a perfect square on the left side: (x + -6)(x + -6) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + -6) equal to 8.062257748 and -8.062257748.Subproblem 1
x + -6 = 8.062257748 Simplifying x + -6 = 8.062257748 Reorder the terms: -6 + x = 8.062257748 Solving -6 + x = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.062257748 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.062257748 + 6 x = 8.062257748 + 6 Combine like terms: 8.062257748 + 6 = 14.062257748 x = 14.062257748 Simplifying x = 14.062257748Subproblem 2
x + -6 = -8.062257748 Simplifying x + -6 = -8.062257748 Reorder the terms: -6 + x = -8.062257748 Solving -6 + x = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.062257748 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.062257748 + 6 x = -8.062257748 + 6 Combine like terms: -8.062257748 + 6 = -2.062257748 x = -2.062257748 Simplifying x = -2.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.062257748, -2.062257748}
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