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Simplifying 8x2 + 3x + -9 = 1 Reorder the terms: -9 + 3x + 8x2 = 1 Solving -9 + 3x + 8x2 = 1 Solving for variable 'x'. Reorder the terms: -9 + -1 + 3x + 8x2 = 1 + -1 Combine like terms: -9 + -1 = -10 -10 + 3x + 8x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -10 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.25 + 0.375x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.375x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.375x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.375x + x2 = 0 + 1.25 0.375x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.375x + x2 = 1.25 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 = 1.25 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 1.25 + 0.03515625 Combine like terms: 1.25 + 0.03515625 = 1.28515625 0.03515625 + 0.375x + x2 = 1.28515625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 1.28515625 Calculate the square root of the right side: 1.133647322 Break this problem into two subproblems by setting (x + 0.1875) equal to 1.133647322 and -1.133647322.Subproblem 1
x + 0.1875 = 1.133647322 Simplifying x + 0.1875 = 1.133647322 Reorder the terms: 0.1875 + x = 1.133647322 Solving 0.1875 + x = 1.133647322 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 = 1.133647322 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.133647322 + -0.1875 x = 1.133647322 + -0.1875 Combine like terms: 1.133647322 + -0.1875 = 0.946147322 x = 0.946147322 Simplifying x = 0.946147322Subproblem 2
x + 0.1875 = -1.133647322 Simplifying x + 0.1875 = -1.133647322 Reorder the terms: 0.1875 + x = -1.133647322 Solving 0.1875 + x = -1.133647322 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 = -1.133647322 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.133647322 + -0.1875 x = -1.133647322 + -0.1875 Combine like terms: -1.133647322 + -0.1875 = -1.321147322 x = -1.321147322 Simplifying x = -1.321147322Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.946147322, -1.321147322}
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