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Simplifying (x + 3)(x + 3) + x2 = 10.8166538264 Reorder the terms: (3 + x)(x + 3) + x2 = 10.8166538264 Reorder the terms: (3 + x)(3 + x) + x2 = 10.8166538264 Multiply (3 + x) * (3 + x) (3(3 + x) + x(3 + x)) + x2 = 10.8166538264 ((3 * 3 + x * 3) + x(3 + x)) + x2 = 10.8166538264 ((9 + 3x) + x(3 + x)) + x2 = 10.8166538264 (9 + 3x + (3 * x + x * x)) + x2 = 10.8166538264 (9 + 3x + (3x + x2)) + x2 = 10.8166538264 Combine like terms: 3x + 3x = 6x (9 + 6x + x2) + x2 = 10.8166538264 Combine like terms: x2 + x2 = 2x2 9 + 6x + 2x2 = 10.8166538264 Solving 9 + 6x + 2x2 = 10.8166538264 Solving for variable 'x'. Reorder the terms: 9 + -10.8166538264 + 6x + 2x2 = 10.8166538264 + -10.8166538264 Combine like terms: 9 + -10.8166538264 = -1.8166538264 -1.8166538264 + 6x + 2x2 = 10.8166538264 + -10.8166538264 Combine like terms: 10.8166538264 + -10.8166538264 = 0.0000000000 -1.8166538264 + 6x + 2x2 = 0.0000000000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.9083269132 + 3x + x2 = 0.0000000000 Move the constant term to the right: Add '0.9083269132' to each side of the equation. -0.9083269132 + 3x + 0.9083269132 + x2 = 0.0000000000 + 0.9083269132 Reorder the terms: -0.9083269132 + 0.9083269132 + 3x + x2 = 0.0000000000 + 0.9083269132 Combine like terms: -0.9083269132 + 0.9083269132 = 0.0000000000 0.0000000000 + 3x + x2 = 0.0000000000 + 0.9083269132 3x + x2 = 0.0000000000 + 0.9083269132 Combine like terms: 0.0000000000 + 0.9083269132 = 0.9083269132 3x + x2 = 0.9083269132 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 0.9083269132 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.9083269132 + 2.25 Combine like terms: 0.9083269132 + 2.25 = 3.1583269132 2.25 + 3x + x2 = 3.1583269132 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.1583269132 Calculate the square root of the right side: 1.777168229 Break this problem into two subproblems by setting (x + 1.5) equal to 1.777168229 and -1.777168229.Subproblem 1
x + 1.5 = 1.777168229 Simplifying x + 1.5 = 1.777168229 Reorder the terms: 1.5 + x = 1.777168229 Solving 1.5 + x = 1.777168229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.777168229 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.777168229 + -1.5 x = 1.777168229 + -1.5 Combine like terms: 1.777168229 + -1.5 = 0.277168229 x = 0.277168229 Simplifying x = 0.277168229Subproblem 2
x + 1.5 = -1.777168229 Simplifying x + 1.5 = -1.777168229 Reorder the terms: 1.5 + x = -1.777168229 Solving 1.5 + x = -1.777168229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.777168229 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.777168229 + -1.5 x = -1.777168229 + -1.5 Combine like terms: -1.777168229 + -1.5 = -3.277168229 x = -3.277168229 Simplifying x = -3.277168229Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.277168229, -3.277168229}
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