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Simplifying 7x(6x + 6) = 1 Reorder the terms: 7x(6 + 6x) = 1 (6 * 7x + 6x * 7x) = 1 (42x + 42x2) = 1 Solving 42x + 42x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 42x + 42x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 42x + 42x2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.02380952381 + x + x2 = 0 Move the constant term to the right: Add '0.02380952381' to each side of the equation. -0.02380952381 + x + 0.02380952381 + x2 = 0 + 0.02380952381 Reorder the terms: -0.02380952381 + 0.02380952381 + x + x2 = 0 + 0.02380952381 Combine like terms: -0.02380952381 + 0.02380952381 = 0.00000000000 0.00000000000 + x + x2 = 0 + 0.02380952381 x + x2 = 0 + 0.02380952381 Combine like terms: 0 + 0.02380952381 = 0.02380952381 x + x2 = 0.02380952381 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.02380952381 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.02380952381 + 0.25 Combine like terms: 0.02380952381 + 0.25 = 0.27380952381 1.25 + x2 = 0.27380952381 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.27380952381 Calculate the square root of the right side: 0.523268118 Break this problem into two subproblems by setting (x + 0.5) equal to 0.523268118 and -0.523268118.Subproblem 1
x + 0.5 = 0.523268118 Simplifying x + 0.5 = 0.523268118 Reorder the terms: 0.5 + x = 0.523268118 Solving 0.5 + x = 0.523268118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.523268118 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.523268118 + -0.5 x = 0.523268118 + -0.5 Combine like terms: 0.523268118 + -0.5 = 0.023268118 x = 0.023268118 Simplifying x = 0.023268118Subproblem 2
x + 0.5 = -0.523268118 Simplifying x + 0.5 = -0.523268118 Reorder the terms: 0.5 + x = -0.523268118 Solving 0.5 + x = -0.523268118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.523268118 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.523268118 + -0.5 x = -0.523268118 + -0.5 Combine like terms: -0.523268118 + -0.5 = -1.023268118 x = -1.023268118 Simplifying x = -1.023268118Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.023268118, -1.023268118}
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