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Simplifying 8x2 + -6x + -26 = -2x2 + -9x Reorder the terms: -26 + -6x + 8x2 = -2x2 + -9x Reorder the terms: -26 + -6x + 8x2 = -9x + -2x2 Solving -26 + -6x + 8x2 = -9x + -2x2 Solving for variable 'x'. Reorder the terms: -26 + -6x + 9x + 8x2 + 2x2 = -9x + -2x2 + 9x + 2x2 Combine like terms: -6x + 9x = 3x -26 + 3x + 8x2 + 2x2 = -9x + -2x2 + 9x + 2x2 Combine like terms: 8x2 + 2x2 = 10x2 -26 + 3x + 10x2 = -9x + -2x2 + 9x + 2x2 Reorder the terms: -26 + 3x + 10x2 = -9x + 9x + -2x2 + 2x2 Combine like terms: -9x + 9x = 0 -26 + 3x + 10x2 = 0 + -2x2 + 2x2 -26 + 3x + 10x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -26 + 3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.6 + 0.3x + x2 = 0.0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 0.3x + 2.6 + x2 = 0.0 + 2.6 Reorder the terms: -2.6 + 2.6 + 0.3x + x2 = 0.0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 0.3x + x2 = 0.0 + 2.6 0.3x + x2 = 0.0 + 2.6 Combine like terms: 0.0 + 2.6 = 2.6 0.3x + x2 = 2.6 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 2.6 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 2.6 + 0.0225 Combine like terms: 2.6 + 0.0225 = 2.6225 0.0225 + 0.3x + x2 = 2.6225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 2.6225 Calculate the square root of the right side: 1.619413474 Break this problem into two subproblems by setting (x + 0.15) equal to 1.619413474 and -1.619413474.Subproblem 1
x + 0.15 = 1.619413474 Simplifying x + 0.15 = 1.619413474 Reorder the terms: 0.15 + x = 1.619413474 Solving 0.15 + x = 1.619413474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 1.619413474 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 1.619413474 + -0.15 x = 1.619413474 + -0.15 Combine like terms: 1.619413474 + -0.15 = 1.469413474 x = 1.469413474 Simplifying x = 1.469413474Subproblem 2
x + 0.15 = -1.619413474 Simplifying x + 0.15 = -1.619413474 Reorder the terms: 0.15 + x = -1.619413474 Solving 0.15 + x = -1.619413474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -1.619413474 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -1.619413474 + -0.15 x = -1.619413474 + -0.15 Combine like terms: -1.619413474 + -0.15 = -1.769413474 x = -1.769413474 Simplifying x = -1.769413474Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.469413474, -1.769413474}
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