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Simplifying x(2x + -3) = 26 Reorder the terms: x(-3 + 2x) = 26 (-3 * x + 2x * x) = 26 (-3x + 2x2) = 26 Solving -3x + 2x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + -3x + 2x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + -1.5x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -1.5x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -1.5x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1.5x + x2 = 0 + 13 -1.5x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -1.5x + x2 = 13 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 13 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 13 + 0.5625 Combine like terms: 13 + 0.5625 = 13.5625 0.5625 + -1.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + -0.75) equal to 3.682729966 and -3.682729966.Subproblem 1
x + -0.75 = 3.682729966 Simplifying x + -0.75 = 3.682729966 Reorder the terms: -0.75 + x = 3.682729966 Solving -0.75 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 3.682729966 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.682729966 + 0.75 x = 3.682729966 + 0.75 Combine like terms: 3.682729966 + 0.75 = 4.432729966 x = 4.432729966 Simplifying x = 4.432729966Subproblem 2
x + -0.75 = -3.682729966 Simplifying x + -0.75 = -3.682729966 Reorder the terms: -0.75 + x = -3.682729966 Solving -0.75 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -3.682729966 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.682729966 + 0.75 x = -3.682729966 + 0.75 Combine like terms: -3.682729966 + 0.75 = -2.932729966 x = -2.932729966 Simplifying x = -2.932729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.432729966, -2.932729966}
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