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Simplifying x2 + 4x + 4 = 2x2 + 17x + -30 Reorder the terms: 4 + 4x + x2 = 2x2 + 17x + -30 Reorder the terms: 4 + 4x + x2 = -30 + 17x + 2x2 Solving 4 + 4x + x2 = -30 + 17x + 2x2 Solving for variable 'x'. Reorder the terms: 4 + 30 + 4x + -17x + x2 + -2x2 = -30 + 17x + 2x2 + 30 + -17x + -2x2 Combine like terms: 4 + 30 = 34 34 + 4x + -17x + x2 + -2x2 = -30 + 17x + 2x2 + 30 + -17x + -2x2 Combine like terms: 4x + -17x = -13x 34 + -13x + x2 + -2x2 = -30 + 17x + 2x2 + 30 + -17x + -2x2 Combine like terms: x2 + -2x2 = -1x2 34 + -13x + -1x2 = -30 + 17x + 2x2 + 30 + -17x + -2x2 Reorder the terms: 34 + -13x + -1x2 = -30 + 30 + 17x + -17x + 2x2 + -2x2 Combine like terms: -30 + 30 = 0 34 + -13x + -1x2 = 0 + 17x + -17x + 2x2 + -2x2 34 + -13x + -1x2 = 17x + -17x + 2x2 + -2x2 Combine like terms: 17x + -17x = 0 34 + -13x + -1x2 = 0 + 2x2 + -2x2 34 + -13x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 34 + -13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -34 + 13x + x2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + 13x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 13x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 13x + x2 = 0 + 34 13x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 13x + x2 = 34 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 34 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 34 + 42.25 Combine like terms: 34 + 42.25 = 76.25 42.25 + 13x + x2 = 76.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (x + 6.5) equal to 8.732124598 and -8.732124598.Subproblem 1
x + 6.5 = 8.732124598 Simplifying x + 6.5 = 8.732124598 Reorder the terms: 6.5 + x = 8.732124598 Solving 6.5 + x = 8.732124598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 8.732124598 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 8.732124598 + -6.5 x = 8.732124598 + -6.5 Combine like terms: 8.732124598 + -6.5 = 2.232124598 x = 2.232124598 Simplifying x = 2.232124598Subproblem 2
x + 6.5 = -8.732124598 Simplifying x + 6.5 = -8.732124598 Reorder the terms: 6.5 + x = -8.732124598 Solving 6.5 + x = -8.732124598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -8.732124598 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -8.732124598 + -6.5 x = -8.732124598 + -6.5 Combine like terms: -8.732124598 + -6.5 = -15.232124598 x = -15.232124598 Simplifying x = -15.232124598Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.232124598, -15.232124598}
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