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Simplifying 5x2 + -3x + -222 = 0 Reorder the terms: -222 + -3x + 5x2 = 0 Solving -222 + -3x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -44.4 + -0.6x + x2 = 0 Move the constant term to the right: Add '44.4' to each side of the equation. -44.4 + -0.6x + 44.4 + x2 = 0 + 44.4 Reorder the terms: -44.4 + 44.4 + -0.6x + x2 = 0 + 44.4 Combine like terms: -44.4 + 44.4 = 0.0 0.0 + -0.6x + x2 = 0 + 44.4 -0.6x + x2 = 0 + 44.4 Combine like terms: 0 + 44.4 = 44.4 -0.6x + x2 = 44.4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 44.4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 44.4 + 0.09 Combine like terms: 44.4 + 0.09 = 44.49 0.09 + -0.6x + x2 = 44.49 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 44.49 Calculate the square root of the right side: 6.670082458 Break this problem into two subproblems by setting (x + -0.3) equal to 6.670082458 and -6.670082458.Subproblem 1
x + -0.3 = 6.670082458 Simplifying x + -0.3 = 6.670082458 Reorder the terms: -0.3 + x = 6.670082458 Solving -0.3 + x = 6.670082458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 6.670082458 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 6.670082458 + 0.3 x = 6.670082458 + 0.3 Combine like terms: 6.670082458 + 0.3 = 6.970082458 x = 6.970082458 Simplifying x = 6.970082458Subproblem 2
x + -0.3 = -6.670082458 Simplifying x + -0.3 = -6.670082458 Reorder the terms: -0.3 + x = -6.670082458 Solving -0.3 + x = -6.670082458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -6.670082458 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -6.670082458 + 0.3 x = -6.670082458 + 0.3 Combine like terms: -6.670082458 + 0.3 = -6.370082458 x = -6.370082458 Simplifying x = -6.370082458Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.970082458, -6.370082458}
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