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Simplifying (2x + -1)(2x + -1) + 7 = 21 Reorder the terms: (-1 + 2x)(2x + -1) + 7 = 21 Reorder the terms: (-1 + 2x)(-1 + 2x) + 7 = 21 Multiply (-1 + 2x) * (-1 + 2x) (-1(-1 + 2x) + 2x * (-1 + 2x)) + 7 = 21 ((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) + 7 = 21 ((1 + -2x) + 2x * (-1 + 2x)) + 7 = 21 (1 + -2x + (-1 * 2x + 2x * 2x)) + 7 = 21 (1 + -2x + (-2x + 4x2)) + 7 = 21 Combine like terms: -2x + -2x = -4x (1 + -4x + 4x2) + 7 = 21 Reorder the terms: 1 + 7 + -4x + 4x2 = 21 Combine like terms: 1 + 7 = 8 8 + -4x + 4x2 = 21 Solving 8 + -4x + 4x2 = 21 Solving for variable 'x'. Reorder the terms: 8 + -21 + -4x + 4x2 = 21 + -21 Combine like terms: 8 + -21 = -13 -13 + -4x + 4x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -13 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + -1x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -1x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -1x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -1x + x2 = 0 + 3.25 -1x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -1x + x2 = 3.25 The x term is -1x. 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. -1x + 0.25 + x2 = 3.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3.25 + 0.25 Combine like terms: 3.25 + 0.25 = 3.5 0.25 + -1x + x2 = 3.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + -0.5) equal to 1.870828693 and -1.870828693.Subproblem 1
x + -0.5 = 1.870828693 Simplifying x + -0.5 = 1.870828693 Reorder the terms: -0.5 + x = 1.870828693 Solving -0.5 + x = 1.870828693 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 = 1.870828693 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.870828693 + 0.5 x = 1.870828693 + 0.5 Combine like terms: 1.870828693 + 0.5 = 2.370828693 x = 2.370828693 Simplifying x = 2.370828693Subproblem 2
x + -0.5 = -1.870828693 Simplifying x + -0.5 = -1.870828693 Reorder the terms: -0.5 + x = -1.870828693 Solving -0.5 + x = -1.870828693 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 = -1.870828693 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.870828693 + 0.5 x = -1.870828693 + 0.5 Combine like terms: -1.870828693 + 0.5 = -1.370828693 x = -1.370828693 Simplifying x = -1.370828693Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.370828693, -1.370828693}
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