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Simplifying (3x2 + 9x + -7) + -1(12x2 + -12x + 4) = 0 Reorder the terms: (-7 + 9x + 3x2) + -1(12x2 + -12x + 4) = 0 Remove parenthesis around (-7 + 9x + 3x2) -7 + 9x + 3x2 + -1(12x2 + -12x + 4) = 0 Reorder the terms: -7 + 9x + 3x2 + -1(4 + -12x + 12x2) = 0 -7 + 9x + 3x2 + (4 * -1 + -12x * -1 + 12x2 * -1) = 0 -7 + 9x + 3x2 + (-4 + 12x + -12x2) = 0 Reorder the terms: -7 + -4 + 9x + 12x + 3x2 + -12x2 = 0 Combine like terms: -7 + -4 = -11 -11 + 9x + 12x + 3x2 + -12x2 = 0 Combine like terms: 9x + 12x = 21x -11 + 21x + 3x2 + -12x2 = 0 Combine like terms: 3x2 + -12x2 = -9x2 -11 + 21x + -9x2 = 0 Solving -11 + 21x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 1.222222222 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '-1.222222222' to each side of the equation. 1.222222222 + -2.333333333x + -1.222222222 + x2 = 0 + -1.222222222 Reorder the terms: 1.222222222 + -1.222222222 + -2.333333333x + x2 = 0 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + -2.333333333x + x2 = 0 + -1.222222222 -2.333333333x + x2 = 0 + -1.222222222 Combine like terms: 0 + -1.222222222 = -1.222222222 -2.333333333x + x2 = -1.222222222 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = -1.222222222 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = -1.222222222 + 1.361111112 Combine like terms: -1.222222222 + 1.361111112 = 0.13888889 1.361111112 + -2.333333333x + x2 = 0.13888889 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 0.13888889 Calculate the square root of the right side: 0.372677998 Break this problem into two subproblems by setting (x + -1.166666667) equal to 0.372677998 and -0.372677998.Subproblem 1
x + -1.166666667 = 0.372677998 Simplifying x + -1.166666667 = 0.372677998 Reorder the terms: -1.166666667 + x = 0.372677998 Solving -1.166666667 + x = 0.372677998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 0.372677998 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 0.372677998 + 1.166666667 x = 0.372677998 + 1.166666667 Combine like terms: 0.372677998 + 1.166666667 = 1.539344665 x = 1.539344665 Simplifying x = 1.539344665Subproblem 2
x + -1.166666667 = -0.372677998 Simplifying x + -1.166666667 = -0.372677998 Reorder the terms: -1.166666667 + x = -0.372677998 Solving -1.166666667 + x = -0.372677998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -0.372677998 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -0.372677998 + 1.166666667 x = -0.372677998 + 1.166666667 Combine like terms: -0.372677998 + 1.166666667 = 0.793988669 x = 0.793988669 Simplifying x = 0.793988669Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.539344665, 0.793988669}
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