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Simplifying 23.174x2 + -2x + -11.087 = 0 Reorder the terms: -11.087 + -2x + 23.174x2 = 0 Solving -11.087 + -2x + 23.174x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23.174 the coefficient of the squared term: Divide each side by '23.174'. -0.478424096 + -0.08630361612x + x2 = 0 Move the constant term to the right: Add '0.478424096' to each side of the equation. -0.478424096 + -0.08630361612x + 0.478424096 + x2 = 0 + 0.478424096 Reorder the terms: -0.478424096 + 0.478424096 + -0.08630361612x + x2 = 0 + 0.478424096 Combine like terms: -0.478424096 + 0.478424096 = 0.000000000 0.000000000 + -0.08630361612x + x2 = 0 + 0.478424096 -0.08630361612x + x2 = 0 + 0.478424096 Combine like terms: 0 + 0.478424096 = 0.478424096 -0.08630361612x + x2 = 0.478424096 The x term is -0.08630361612x. Take half its coefficient (-0.04315180806). Square it (0.001862078539) and add it to both sides. Add '0.001862078539' to each side of the equation. -0.08630361612x + 0.001862078539 + x2 = 0.478424096 + 0.001862078539 Reorder the terms: 0.001862078539 + -0.08630361612x + x2 = 0.478424096 + 0.001862078539 Combine like terms: 0.478424096 + 0.001862078539 = 0.480286174539 0.001862078539 + -0.08630361612x + x2 = 0.480286174539 Factor a perfect square on the left side: (x + -0.04315180806)(x + -0.04315180806) = 0.480286174539 Calculate the square root of the right side: 0.693026821 Break this problem into two subproblems by setting (x + -0.04315180806) equal to 0.693026821 and -0.693026821.Subproblem 1
x + -0.04315180806 = 0.693026821 Simplifying x + -0.04315180806 = 0.693026821 Reorder the terms: -0.04315180806 + x = 0.693026821 Solving -0.04315180806 + x = 0.693026821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04315180806' to each side of the equation. -0.04315180806 + 0.04315180806 + x = 0.693026821 + 0.04315180806 Combine like terms: -0.04315180806 + 0.04315180806 = 0.00000000000 0.00000000000 + x = 0.693026821 + 0.04315180806 x = 0.693026821 + 0.04315180806 Combine like terms: 0.693026821 + 0.04315180806 = 0.73617862906 x = 0.73617862906 Simplifying x = 0.73617862906Subproblem 2
x + -0.04315180806 = -0.693026821 Simplifying x + -0.04315180806 = -0.693026821 Reorder the terms: -0.04315180806 + x = -0.693026821 Solving -0.04315180806 + x = -0.693026821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04315180806' to each side of the equation. -0.04315180806 + 0.04315180806 + x = -0.693026821 + 0.04315180806 Combine like terms: -0.04315180806 + 0.04315180806 = 0.00000000000 0.00000000000 + x = -0.693026821 + 0.04315180806 x = -0.693026821 + 0.04315180806 Combine like terms: -0.693026821 + 0.04315180806 = -0.64987501294 x = -0.64987501294 Simplifying x = -0.64987501294Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.73617862906, -0.64987501294}
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