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Simplifying 2x2 + -23x = 7x2 + -6x + -8 Reorder the terms: -23x + 2x2 = 7x2 + -6x + -8 Reorder the terms: -23x + 2x2 = -8 + -6x + 7x2 Solving -23x + 2x2 = -8 + -6x + 7x2 Solving for variable 'x'. Reorder the terms: 8 + -23x + 6x + 2x2 + -7x2 = -8 + -6x + 7x2 + 8 + 6x + -7x2 Combine like terms: -23x + 6x = -17x 8 + -17x + 2x2 + -7x2 = -8 + -6x + 7x2 + 8 + 6x + -7x2 Combine like terms: 2x2 + -7x2 = -5x2 8 + -17x + -5x2 = -8 + -6x + 7x2 + 8 + 6x + -7x2 Reorder the terms: 8 + -17x + -5x2 = -8 + 8 + -6x + 6x + 7x2 + -7x2 Combine like terms: -8 + 8 = 0 8 + -17x + -5x2 = 0 + -6x + 6x + 7x2 + -7x2 8 + -17x + -5x2 = -6x + 6x + 7x2 + -7x2 Combine like terms: -6x + 6x = 0 8 + -17x + -5x2 = 0 + 7x2 + -7x2 8 + -17x + -5x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 8 + -17x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.6 + 3.4x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 3.4x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 3.4x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 3.4x + x2 = 0 + 1.6 3.4x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 3.4x + x2 = 1.6 The x term is 3.4x. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4x + 2.89 + x2 = 1.6 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = 1.6 + 2.89 Combine like terms: 1.6 + 2.89 = 4.49 2.89 + 3.4x + x2 = 4.49 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 4.49 Calculate the square root of the right side: 2.11896201 Break this problem into two subproblems by setting (x + 1.7) equal to 2.11896201 and -2.11896201.Subproblem 1
x + 1.7 = 2.11896201 Simplifying x + 1.7 = 2.11896201 Reorder the terms: 1.7 + x = 2.11896201 Solving 1.7 + x = 2.11896201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = 2.11896201 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 2.11896201 + -1.7 x = 2.11896201 + -1.7 Combine like terms: 2.11896201 + -1.7 = 0.41896201 x = 0.41896201 Simplifying x = 0.41896201Subproblem 2
x + 1.7 = -2.11896201 Simplifying x + 1.7 = -2.11896201 Reorder the terms: 1.7 + x = -2.11896201 Solving 1.7 + x = -2.11896201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = -2.11896201 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -2.11896201 + -1.7 x = -2.11896201 + -1.7 Combine like terms: -2.11896201 + -1.7 = -3.81896201 x = -3.81896201 Simplifying x = -3.81896201Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.41896201, -3.81896201}
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