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Simplifying 5x(x + -3) + -2x = 6 Reorder the terms: 5x(-3 + x) + -2x = 6 (-3 * 5x + x * 5x) + -2x = 6 (-15x + 5x2) + -2x = 6 Reorder the terms: -15x + -2x + 5x2 = 6 Combine like terms: -15x + -2x = -17x -17x + 5x2 = 6 Solving -17x + 5x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + -17x + 5x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -3.4x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -3.4x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -3.4x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -3.4x + x2 = 0 + 1.2 -3.4x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -3.4x + x2 = 1.2 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 = 1.2 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 1.2 + 2.89 Combine like terms: 1.2 + 2.89 = 4.09 2.89 + -3.4x + x2 = 4.09 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (x + -1.7) equal to 2.022374842 and -2.022374842.Subproblem 1
x + -1.7 = 2.022374842 Simplifying x + -1.7 = 2.022374842 Reorder the terms: -1.7 + x = 2.022374842 Solving -1.7 + x = 2.022374842 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 = 2.022374842 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 2.022374842 + 1.7 x = 2.022374842 + 1.7 Combine like terms: 2.022374842 + 1.7 = 3.722374842 x = 3.722374842 Simplifying x = 3.722374842Subproblem 2
x + -1.7 = -2.022374842 Simplifying x + -1.7 = -2.022374842 Reorder the terms: -1.7 + x = -2.022374842 Solving -1.7 + x = -2.022374842 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 = -2.022374842 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -2.022374842 + 1.7 x = -2.022374842 + 1.7 Combine like terms: -2.022374842 + 1.7 = -0.322374842 x = -0.322374842 Simplifying x = -0.322374842Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.722374842, -0.322374842}
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