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Simplifying 6(x + 2) + -1x = 4x(x + 4) + 7 Reorder the terms: 6(2 + x) + -1x = 4x(x + 4) + 7 (2 * 6 + x * 6) + -1x = 4x(x + 4) + 7 (12 + 6x) + -1x = 4x(x + 4) + 7 Combine like terms: 6x + -1x = 5x 12 + 5x = 4x(x + 4) + 7 Reorder the terms: 12 + 5x = 4x(4 + x) + 7 12 + 5x = (4 * 4x + x * 4x) + 7 12 + 5x = (16x + 4x2) + 7 Reorder the terms: 12 + 5x = 7 + 16x + 4x2 Solving 12 + 5x = 7 + 16x + 4x2 Solving for variable 'x'. Reorder the terms: 12 + -7 + 5x + -16x + -4x2 = 7 + 16x + 4x2 + -7 + -16x + -4x2 Combine like terms: 12 + -7 = 5 5 + 5x + -16x + -4x2 = 7 + 16x + 4x2 + -7 + -16x + -4x2 Combine like terms: 5x + -16x = -11x 5 + -11x + -4x2 = 7 + 16x + 4x2 + -7 + -16x + -4x2 Reorder the terms: 5 + -11x + -4x2 = 7 + -7 + 16x + -16x + 4x2 + -4x2 Combine like terms: 7 + -7 = 0 5 + -11x + -4x2 = 0 + 16x + -16x + 4x2 + -4x2 5 + -11x + -4x2 = 16x + -16x + 4x2 + -4x2 Combine like terms: 16x + -16x = 0 5 + -11x + -4x2 = 0 + 4x2 + -4x2 5 + -11x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 5 + -11x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + 2.75x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 2.75x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 2.75x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 2.75x + x2 = 0 + 1.25 2.75x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 2.75x + x2 = 1.25 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 1.25 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 1.25 + 1.890625 Combine like terms: 1.25 + 1.890625 = 3.140625 1.890625 + 2.75x + x2 = 3.140625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + 1.375) equal to 1.77218086 and -1.77218086.Subproblem 1
x + 1.375 = 1.77218086 Simplifying x + 1.375 = 1.77218086 Reorder the terms: 1.375 + x = 1.77218086 Solving 1.375 + x = 1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 1.77218086 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 1.77218086 + -1.375 x = 1.77218086 + -1.375 Combine like terms: 1.77218086 + -1.375 = 0.39718086 x = 0.39718086 Simplifying x = 0.39718086Subproblem 2
x + 1.375 = -1.77218086 Simplifying x + 1.375 = -1.77218086 Reorder the terms: 1.375 + x = -1.77218086 Solving 1.375 + x = -1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -1.77218086 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -1.77218086 + -1.375 x = -1.77218086 + -1.375 Combine like terms: -1.77218086 + -1.375 = -3.14718086 x = -3.14718086 Simplifying x = -3.14718086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.39718086, -3.14718086}
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