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Simplifying x(10x + -13) = 27 Reorder the terms: x(-13 + 10x) = 27 (-13 * x + 10x * x) = 27 (-13x + 10x2) = 27 Solving -13x + 10x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + -13x + 10x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -13x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.7 + -1.3x + x2 = 0 Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + -1.3x + 2.7 + x2 = 0 + 2.7 Reorder the terms: -2.7 + 2.7 + -1.3x + x2 = 0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + -1.3x + x2 = 0 + 2.7 -1.3x + x2 = 0 + 2.7 Combine like terms: 0 + 2.7 = 2.7 -1.3x + x2 = 2.7 The x term is -1.3x. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x + 0.4225 + x2 = 2.7 + 0.4225 Reorder the terms: 0.4225 + -1.3x + x2 = 2.7 + 0.4225 Combine like terms: 2.7 + 0.4225 = 3.1225 0.4225 + -1.3x + x2 = 3.1225 Factor a perfect square on the left side: (x + -0.65)(x + -0.65) = 3.1225 Calculate the square root of the right side: 1.767059705 Break this problem into two subproblems by setting (x + -0.65) equal to 1.767059705 and -1.767059705.Subproblem 1
x + -0.65 = 1.767059705 Simplifying x + -0.65 = 1.767059705 Reorder the terms: -0.65 + x = 1.767059705 Solving -0.65 + x = 1.767059705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = 1.767059705 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = 1.767059705 + 0.65 x = 1.767059705 + 0.65 Combine like terms: 1.767059705 + 0.65 = 2.417059705 x = 2.417059705 Simplifying x = 2.417059705Subproblem 2
x + -0.65 = -1.767059705 Simplifying x + -0.65 = -1.767059705 Reorder the terms: -0.65 + x = -1.767059705 Solving -0.65 + x = -1.767059705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = -1.767059705 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = -1.767059705 + 0.65 x = -1.767059705 + 0.65 Combine like terms: -1.767059705 + 0.65 = -1.117059705 x = -1.117059705 Simplifying x = -1.117059705Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.417059705, -1.117059705}
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