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Simplifying (x + -12)(x + 6) + 10 = 0 Reorder the terms: (-12 + x)(x + 6) + 10 = 0 Reorder the terms: (-12 + x)(6 + x) + 10 = 0 Multiply (-12 + x) * (6 + x) (-12(6 + x) + x(6 + x)) + 10 = 0 ((6 * -12 + x * -12) + x(6 + x)) + 10 = 0 ((-72 + -12x) + x(6 + x)) + 10 = 0 (-72 + -12x + (6 * x + x * x)) + 10 = 0 (-72 + -12x + (6x + x2)) + 10 = 0 Combine like terms: -12x + 6x = -6x (-72 + -6x + x2) + 10 = 0 Reorder the terms: -72 + 10 + -6x + x2 = 0 Combine like terms: -72 + 10 = -62 -62 + -6x + x2 = 0 Solving -62 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + -6x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -6x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -6x + x2 = 0 + 62 -6x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -6x + x2 = 62 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 = 62 + 9 Reorder the terms: 9 + -6x + x2 = 62 + 9 Combine like terms: 62 + 9 = 71 9 + -6x + x2 = 71 Factor a perfect square on the left side: (x + -3)(x + -3) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + -3) equal to 8.426149773 and -8.426149773.Subproblem 1
x + -3 = 8.426149773 Simplifying x + -3 = 8.426149773 Reorder the terms: -3 + x = 8.426149773 Solving -3 + x = 8.426149773 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 = 8.426149773 + 3 Combine like terms: -3 + 3 = 0 0 + x = 8.426149773 + 3 x = 8.426149773 + 3 Combine like terms: 8.426149773 + 3 = 11.426149773 x = 11.426149773 Simplifying x = 11.426149773Subproblem 2
x + -3 = -8.426149773 Simplifying x + -3 = -8.426149773 Reorder the terms: -3 + x = -8.426149773 Solving -3 + x = -8.426149773 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 = -8.426149773 + 3 Combine like terms: -3 + 3 = 0 0 + x = -8.426149773 + 3 x = -8.426149773 + 3 Combine like terms: -8.426149773 + 3 = -5.426149773 x = -5.426149773 Simplifying x = -5.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.426149773, -5.426149773}
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