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Simplifying 8x2 + 3x + -5 = 36 Reorder the terms: -5 + 3x + 8x2 = 36 Solving -5 + 3x + 8x2 = 36 Solving for variable 'x'. Reorder the terms: -5 + -36 + 3x + 8x2 = 36 + -36 Combine like terms: -5 + -36 = -41 -41 + 3x + 8x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -41 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.125 + 0.375x + x2 = 0 Move the constant term to the right: Add '5.125' to each side of the equation. -5.125 + 0.375x + 5.125 + x2 = 0 + 5.125 Reorder the terms: -5.125 + 5.125 + 0.375x + x2 = 0 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + 0.375x + x2 = 0 + 5.125 0.375x + x2 = 0 + 5.125 Combine like terms: 0 + 5.125 = 5.125 0.375x + x2 = 5.125 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 5.125 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 5.125 + 0.03515625 Combine like terms: 5.125 + 0.03515625 = 5.16015625 0.03515625 + 0.375x + x2 = 5.16015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 5.16015625 Calculate the square root of the right side: 2.271597731 Break this problem into two subproblems by setting (x + 0.1875) equal to 2.271597731 and -2.271597731.Subproblem 1
x + 0.1875 = 2.271597731 Simplifying x + 0.1875 = 2.271597731 Reorder the terms: 0.1875 + x = 2.271597731 Solving 0.1875 + x = 2.271597731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 2.271597731 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 2.271597731 + -0.1875 x = 2.271597731 + -0.1875 Combine like terms: 2.271597731 + -0.1875 = 2.084097731 x = 2.084097731 Simplifying x = 2.084097731Subproblem 2
x + 0.1875 = -2.271597731 Simplifying x + 0.1875 = -2.271597731 Reorder the terms: 0.1875 + x = -2.271597731 Solving 0.1875 + x = -2.271597731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -2.271597731 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -2.271597731 + -0.1875 x = -2.271597731 + -0.1875 Combine like terms: -2.271597731 + -0.1875 = -2.459097731 x = -2.459097731 Simplifying x = -2.459097731Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.084097731, -2.459097731}
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