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Simplifying 56.52 = 3.14(x + 1)(x + 1) Reorder the terms: 56.52 = 3.14(1 + x)(x + 1) Reorder the terms: 56.52 = 3.14(1 + x)(1 + x) Multiply (1 + x) * (1 + x) 56.52 = 3.14(1(1 + x) + x(1 + x)) 56.52 = 3.14((1 * 1 + x * 1) + x(1 + x)) 56.52 = 3.14((1 + 1x) + x(1 + x)) 56.52 = 3.14(1 + 1x + (1 * x + x * x)) 56.52 = 3.14(1 + 1x + (1x + x2)) Combine like terms: 1x + 1x = 2x 56.52 = 3.14(1 + 2x + x2) 56.52 = (1 * 3.14 + 2x * 3.14 + x2 * 3.14) 56.52 = (3.14 + 6.28x + 3.14x2) Solving 56.52 = 3.14 + 6.28x + 3.14x2 Solving for variable 'x'. Combine like terms: 56.52 + -3.14 = 53.38 53.38 + -6.28x + -3.14x2 = 3.14 + 6.28x + 3.14x2 + -3.14 + -6.28x + -3.14x2 Reorder the terms: 53.38 + -6.28x + -3.14x2 = 3.14 + -3.14 + 6.28x + -6.28x + 3.14x2 + -3.14x2 Combine like terms: 3.14 + -3.14 = 0.00 53.38 + -6.28x + -3.14x2 = 0.00 + 6.28x + -6.28x + 3.14x2 + -3.14x2 53.38 + -6.28x + -3.14x2 = 6.28x + -6.28x + 3.14x2 + -3.14x2 Combine like terms: 6.28x + -6.28x = 0.00 53.38 + -6.28x + -3.14x2 = 0.00 + 3.14x2 + -3.14x2 53.38 + -6.28x + -3.14x2 = 3.14x2 + -3.14x2 Combine like terms: 3.14x2 + -3.14x2 = 0.00 53.38 + -6.28x + -3.14x2 = 0.00 Begin completing the square. Divide all terms by -3.14 the coefficient of the squared term: Divide each side by '-3.14'. -17 + 2x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 2x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 2x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2x + x2 = 0 + 17 2x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 2x + x2 = 17 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 = 17 + 1 Reorder the terms: 1 + 2x + x2 = 17 + 1 Combine like terms: 17 + 1 = 18 1 + 2x + x2 = 18 Factor a perfect square on the left side: (x + 1)(x + 1) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 1) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 1 = 4.242640687 Simplifying x + 1 = 4.242640687 Reorder the terms: 1 + x = 4.242640687 Solving 1 + x = 4.242640687 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 = 4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.242640687 + -1 x = 4.242640687 + -1 Combine like terms: 4.242640687 + -1 = 3.242640687 x = 3.242640687 Simplifying x = 3.242640687Subproblem 2
x + 1 = -4.242640687 Simplifying x + 1 = -4.242640687 Reorder the terms: 1 + x = -4.242640687 Solving 1 + x = -4.242640687 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 = -4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.242640687 + -1 x = -4.242640687 + -1 Combine like terms: -4.242640687 + -1 = -5.242640687 x = -5.242640687 Simplifying x = -5.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.242640687, -5.242640687}
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