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Simplifying (5 + -3x)(5 + 3x) = x Multiply (5 + -3x) * (5 + 3x) (5(5 + 3x) + -3x * (5 + 3x)) = x ((5 * 5 + 3x * 5) + -3x * (5 + 3x)) = x ((25 + 15x) + -3x * (5 + 3x)) = x (25 + 15x + (5 * -3x + 3x * -3x)) = x (25 + 15x + (-15x + -9x2)) = x Combine like terms: 15x + -15x = 0 (25 + 0 + -9x2) = x (25 + -9x2) = x Solving 25 + -9x2 = x Solving for variable 'x'. Reorder the terms: 25 + -1x + -9x2 = x + -1x Combine like terms: x + -1x = 0 25 + -1x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2.777777778 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + 0.1111111111x + 2.777777778 + x2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + 0.1111111111x + x2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + 0.1111111111x + x2 = 0 + 2.777777778 0.1111111111x + x2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 0.1111111111x + x2 = 2.777777778 The x term is 0.1111111111x. Take half its coefficient (0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. 0.1111111111x + 0.003086419752 + x2 = 2.777777778 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = 2.777777778 + 0.003086419752 Combine like terms: 2.777777778 + 0.003086419752 = 2.780864197752 0.003086419752 + 0.1111111111x + x2 = 2.780864197752 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = 2.780864197752 Calculate the square root of the right side: 1.667592336 Break this problem into two subproblems by setting (x + 0.05555555555) equal to 1.667592336 and -1.667592336.Subproblem 1
x + 0.05555555555 = 1.667592336 Simplifying x + 0.05555555555 = 1.667592336 Reorder the terms: 0.05555555555 + x = 1.667592336 Solving 0.05555555555 + x = 1.667592336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = 1.667592336 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 1.667592336 + -0.05555555555 x = 1.667592336 + -0.05555555555 Combine like terms: 1.667592336 + -0.05555555555 = 1.61203678045 x = 1.61203678045 Simplifying x = 1.61203678045Subproblem 2
x + 0.05555555555 = -1.667592336 Simplifying x + 0.05555555555 = -1.667592336 Reorder the terms: 0.05555555555 + x = -1.667592336 Solving 0.05555555555 + x = -1.667592336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = -1.667592336 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -1.667592336 + -0.05555555555 x = -1.667592336 + -0.05555555555 Combine like terms: -1.667592336 + -0.05555555555 = -1.72314789155 x = -1.72314789155 Simplifying x = -1.72314789155Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.61203678045, -1.72314789155}
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