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Simplifying 5x(x + -3) = 2x + 1 Reorder the terms: 5x(-3 + x) = 2x + 1 (-3 * 5x + x * 5x) = 2x + 1 (-15x + 5x2) = 2x + 1 Reorder the terms: -15x + 5x2 = 1 + 2x Solving -15x + 5x2 = 1 + 2x Solving for variable 'x'. Reorder the terms: -1 + -15x + -2x + 5x2 = 1 + 2x + -1 + -2x Combine like terms: -15x + -2x = -17x -1 + -17x + 5x2 = 1 + 2x + -1 + -2x Reorder the terms: -1 + -17x + 5x2 = 1 + -1 + 2x + -2x Combine like terms: 1 + -1 = 0 -1 + -17x + 5x2 = 0 + 2x + -2x -1 + -17x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -1 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -3.4x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -3.4x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -3.4x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -3.4x + x2 = 0 + 0.2 -3.4x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -3.4x + x2 = 0.2 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 = 0.2 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 0.2 + 2.89 Combine like terms: 0.2 + 2.89 = 3.09 2.89 + -3.4x + x2 = 3.09 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 3.09 Calculate the square root of the right side: 1.757839583 Break this problem into two subproblems by setting (x + -1.7) equal to 1.757839583 and -1.757839583.Subproblem 1
x + -1.7 = 1.757839583 Simplifying x + -1.7 = 1.757839583 Reorder the terms: -1.7 + x = 1.757839583 Solving -1.7 + x = 1.757839583 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 = 1.757839583 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 1.757839583 + 1.7 x = 1.757839583 + 1.7 Combine like terms: 1.757839583 + 1.7 = 3.457839583 x = 3.457839583 Simplifying x = 3.457839583Subproblem 2
x + -1.7 = -1.757839583 Simplifying x + -1.7 = -1.757839583 Reorder the terms: -1.7 + x = -1.757839583 Solving -1.7 + x = -1.757839583 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 = -1.757839583 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -1.757839583 + 1.7 x = -1.757839583 + 1.7 Combine like terms: -1.757839583 + 1.7 = -0.057839583 x = -0.057839583 Simplifying x = -0.057839583Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.457839583, -0.057839583}
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