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Simplifying 0 = -17.92x2 + 24x + 3 Reorder the terms: 0 = 3 + 24x + -17.92x2 Solving 0 = 3 + 24x + -17.92x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -24x + 17.92x2 = 3 + 24x + -17.92x2 + -3 + -24x + 17.92x2 Reorder the terms: -3 + -24x + 17.92x2 = 3 + -3 + 24x + -24x + -17.92x2 + 17.92x2 Combine like terms: 3 + -3 = 0 -3 + -24x + 17.92x2 = 0 + 24x + -24x + -17.92x2 + 17.92x2 -3 + -24x + 17.92x2 = 24x + -24x + -17.92x2 + 17.92x2 Combine like terms: 24x + -24x = 0 -3 + -24x + 17.92x2 = 0 + -17.92x2 + 17.92x2 -3 + -24x + 17.92x2 = -17.92x2 + 17.92x2 Combine like terms: -17.92x2 + 17.92x2 = 0.00 -3 + -24x + 17.92x2 = 0.00 Begin completing the square. Divide all terms by 17.92 the coefficient of the squared term: Divide each side by '17.92'. -0.1674107143 + -1.339285714x + x2 = 0 Move the constant term to the right: Add '0.1674107143' to each side of the equation. -0.1674107143 + -1.339285714x + 0.1674107143 + x2 = 0 + 0.1674107143 Reorder the terms: -0.1674107143 + 0.1674107143 + -1.339285714x + x2 = 0 + 0.1674107143 Combine like terms: -0.1674107143 + 0.1674107143 = 0.0000000000 0.0000000000 + -1.339285714x + x2 = 0 + 0.1674107143 -1.339285714x + x2 = 0 + 0.1674107143 Combine like terms: 0 + 0.1674107143 = 0.1674107143 -1.339285714x + x2 = 0.1674107143 The x term is -1.339285714x. Take half its coefficient (-0.669642857). Square it (0.4484215559) and add it to both sides. Add '0.4484215559' to each side of the equation. -1.339285714x + 0.4484215559 + x2 = 0.1674107143 + 0.4484215559 Reorder the terms: 0.4484215559 + -1.339285714x + x2 = 0.1674107143 + 0.4484215559 Combine like terms: 0.1674107143 + 0.4484215559 = 0.6158322702 0.4484215559 + -1.339285714x + x2 = 0.6158322702 Factor a perfect square on the left side: (x + -0.669642857)(x + -0.669642857) = 0.6158322702 Calculate the square root of the right side: 0.784749814 Break this problem into two subproblems by setting (x + -0.669642857) equal to 0.784749814 and -0.784749814.Subproblem 1
x + -0.669642857 = 0.784749814 Simplifying x + -0.669642857 = 0.784749814 Reorder the terms: -0.669642857 + x = 0.784749814 Solving -0.669642857 + x = 0.784749814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.669642857' to each side of the equation. -0.669642857 + 0.669642857 + x = 0.784749814 + 0.669642857 Combine like terms: -0.669642857 + 0.669642857 = 0.000000000 0.000000000 + x = 0.784749814 + 0.669642857 x = 0.784749814 + 0.669642857 Combine like terms: 0.784749814 + 0.669642857 = 1.454392671 x = 1.454392671 Simplifying x = 1.454392671Subproblem 2
x + -0.669642857 = -0.784749814 Simplifying x + -0.669642857 = -0.784749814 Reorder the terms: -0.669642857 + x = -0.784749814 Solving -0.669642857 + x = -0.784749814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.669642857' to each side of the equation. -0.669642857 + 0.669642857 + x = -0.784749814 + 0.669642857 Combine like terms: -0.669642857 + 0.669642857 = 0.000000000 0.000000000 + x = -0.784749814 + 0.669642857 x = -0.784749814 + 0.669642857 Combine like terms: -0.784749814 + 0.669642857 = -0.115106957 x = -0.115106957 Simplifying x = -0.115106957Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.454392671, -0.115106957}
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