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Simplifying 9x2 + -3x + -26 = 5x2 + 6x + -7 Reorder the terms: -26 + -3x + 9x2 = 5x2 + 6x + -7 Reorder the terms: -26 + -3x + 9x2 = -7 + 6x + 5x2 Solving -26 + -3x + 9x2 = -7 + 6x + 5x2 Solving for variable 'x'. Reorder the terms: -26 + 7 + -3x + -6x + 9x2 + -5x2 = -7 + 6x + 5x2 + 7 + -6x + -5x2 Combine like terms: -26 + 7 = -19 -19 + -3x + -6x + 9x2 + -5x2 = -7 + 6x + 5x2 + 7 + -6x + -5x2 Combine like terms: -3x + -6x = -9x -19 + -9x + 9x2 + -5x2 = -7 + 6x + 5x2 + 7 + -6x + -5x2 Combine like terms: 9x2 + -5x2 = 4x2 -19 + -9x + 4x2 = -7 + 6x + 5x2 + 7 + -6x + -5x2 Reorder the terms: -19 + -9x + 4x2 = -7 + 7 + 6x + -6x + 5x2 + -5x2 Combine like terms: -7 + 7 = 0 -19 + -9x + 4x2 = 0 + 6x + -6x + 5x2 + -5x2 -19 + -9x + 4x2 = 6x + -6x + 5x2 + -5x2 Combine like terms: 6x + -6x = 0 -19 + -9x + 4x2 = 0 + 5x2 + -5x2 -19 + -9x + 4x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -19 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + -2.25x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -2.25x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -2.25x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -2.25x + x2 = 0 + 4.75 -2.25x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -2.25x + x2 = 4.75 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 4.75 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 4.75 + 1.265625 Combine like terms: 4.75 + 1.265625 = 6.015625 1.265625 + -2.25x + x2 = 6.015625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + -1.125) equal to 2.452677109 and -2.452677109.Subproblem 1
x + -1.125 = 2.452677109 Simplifying x + -1.125 = 2.452677109 Reorder the terms: -1.125 + x = 2.452677109 Solving -1.125 + x = 2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 2.452677109 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 2.452677109 + 1.125 x = 2.452677109 + 1.125 Combine like terms: 2.452677109 + 1.125 = 3.577677109 x = 3.577677109 Simplifying x = 3.577677109Subproblem 2
x + -1.125 = -2.452677109 Simplifying x + -1.125 = -2.452677109 Reorder the terms: -1.125 + x = -2.452677109 Solving -1.125 + x = -2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -2.452677109 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -2.452677109 + 1.125 x = -2.452677109 + 1.125 Combine like terms: -2.452677109 + 1.125 = -1.327677109 x = -1.327677109 Simplifying x = -1.327677109Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.577677109, -1.327677109}
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