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Simplifying 9x + 1 = 3x(2x + 7) + -2 Reorder the terms: 1 + 9x = 3x(2x + 7) + -2 Reorder the terms: 1 + 9x = 3x(7 + 2x) + -2 1 + 9x = (7 * 3x + 2x * 3x) + -2 1 + 9x = (21x + 6x2) + -2 Reorder the terms: 1 + 9x = -2 + 21x + 6x2 Solving 1 + 9x = -2 + 21x + 6x2 Solving for variable 'x'. Reorder the terms: 1 + 2 + 9x + -21x + -6x2 = -2 + 21x + 6x2 + 2 + -21x + -6x2 Combine like terms: 1 + 2 = 3 3 + 9x + -21x + -6x2 = -2 + 21x + 6x2 + 2 + -21x + -6x2 Combine like terms: 9x + -21x = -12x 3 + -12x + -6x2 = -2 + 21x + 6x2 + 2 + -21x + -6x2 Reorder the terms: 3 + -12x + -6x2 = -2 + 2 + 21x + -21x + 6x2 + -6x2 Combine like terms: -2 + 2 = 0 3 + -12x + -6x2 = 0 + 21x + -21x + 6x2 + -6x2 3 + -12x + -6x2 = 21x + -21x + 6x2 + -6x2 Combine like terms: 21x + -21x = 0 3 + -12x + -6x2 = 0 + 6x2 + -6x2 3 + -12x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 3 + -12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -4x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -4x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + -4x + -2x2 = 0 Solving 1 + -4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 2x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2x + x2 = 0 + 0.5 2x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2x + x2 = 0.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.5 + 1 Reorder the terms: 1 + 2x + x2 = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 1 + 2x + x2 = 1.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 1) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 1 = 1.224744871 Simplifying x + 1 = 1.224744871 Reorder the terms: 1 + x = 1.224744871 Solving 1 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.224744871 + -1 x = 1.224744871 + -1 Combine like terms: 1.224744871 + -1 = 0.224744871 x = 0.224744871 Simplifying x = 0.224744871Subproblem 2
x + 1 = -1.224744871 Simplifying x + 1 = -1.224744871 Reorder the terms: 1 + x = -1.224744871 Solving 1 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.224744871 + -1 x = -1.224744871 + -1 Combine like terms: -1.224744871 + -1 = -2.224744871 x = -2.224744871 Simplifying x = -2.224744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.224744871, -2.224744871}Solution
x = {0.224744871, -2.224744871}
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