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Simplifying 12x + -13x(x + 4) = 4x + -6 Reorder the terms: 12x + -13x(4 + x) = 4x + -6 12x + (4 * -13x + x * -13x) = 4x + -6 12x + (-52x + -13x2) = 4x + -6 Combine like terms: 12x + -52x = -40x -40x + -13x2 = 4x + -6 Reorder the terms: -40x + -13x2 = -6 + 4x Solving -40x + -13x2 = -6 + 4x Solving for variable 'x'. Reorder the terms: 6 + -40x + -4x + -13x2 = -6 + 4x + 6 + -4x Combine like terms: -40x + -4x = -44x 6 + -44x + -13x2 = -6 + 4x + 6 + -4x Reorder the terms: 6 + -44x + -13x2 = -6 + 6 + 4x + -4x Combine like terms: -6 + 6 = 0 6 + -44x + -13x2 = 0 + 4x + -4x 6 + -44x + -13x2 = 4x + -4x Combine like terms: 4x + -4x = 0 6 + -44x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.4615384615 + 3.384615385x + x2 = 0 Move the constant term to the right: Add '0.4615384615' to each side of the equation. -0.4615384615 + 3.384615385x + 0.4615384615 + x2 = 0 + 0.4615384615 Reorder the terms: -0.4615384615 + 0.4615384615 + 3.384615385x + x2 = 0 + 0.4615384615 Combine like terms: -0.4615384615 + 0.4615384615 = 0.0000000000 0.0000000000 + 3.384615385x + x2 = 0 + 0.4615384615 3.384615385x + x2 = 0 + 0.4615384615 Combine like terms: 0 + 0.4615384615 = 0.4615384615 3.384615385x + x2 = 0.4615384615 The x term is 3.384615385x. Take half its coefficient (1.692307693). Square it (2.863905328) and add it to both sides. Add '2.863905328' to each side of the equation. 3.384615385x + 2.863905328 + x2 = 0.4615384615 + 2.863905328 Reorder the terms: 2.863905328 + 3.384615385x + x2 = 0.4615384615 + 2.863905328 Combine like terms: 0.4615384615 + 2.863905328 = 3.3254437895 2.863905328 + 3.384615385x + x2 = 3.3254437895 Factor a perfect square on the left side: (x + 1.692307693)(x + 1.692307693) = 3.3254437895 Calculate the square root of the right side: 1.823579938 Break this problem into two subproblems by setting (x + 1.692307693) equal to 1.823579938 and -1.823579938.Subproblem 1
x + 1.692307693 = 1.823579938 Simplifying x + 1.692307693 = 1.823579938 Reorder the terms: 1.692307693 + x = 1.823579938 Solving 1.692307693 + x = 1.823579938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.692307693' to each side of the equation. 1.692307693 + -1.692307693 + x = 1.823579938 + -1.692307693 Combine like terms: 1.692307693 + -1.692307693 = 0.000000000 0.000000000 + x = 1.823579938 + -1.692307693 x = 1.823579938 + -1.692307693 Combine like terms: 1.823579938 + -1.692307693 = 0.131272245 x = 0.131272245 Simplifying x = 0.131272245Subproblem 2
x + 1.692307693 = -1.823579938 Simplifying x + 1.692307693 = -1.823579938 Reorder the terms: 1.692307693 + x = -1.823579938 Solving 1.692307693 + x = -1.823579938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.692307693' to each side of the equation. 1.692307693 + -1.692307693 + x = -1.823579938 + -1.692307693 Combine like terms: 1.692307693 + -1.692307693 = 0.000000000 0.000000000 + x = -1.823579938 + -1.692307693 x = -1.823579938 + -1.692307693 Combine like terms: -1.823579938 + -1.692307693 = -3.515887631 x = -3.515887631 Simplifying x = -3.515887631Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.131272245, -3.515887631}
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