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Simplifying 5x(x + -6) + 4 = 2(x + -7) Reorder the terms: 5x(-6 + x) + 4 = 2(x + -7) (-6 * 5x + x * 5x) + 4 = 2(x + -7) (-30x + 5x2) + 4 = 2(x + -7) Reorder the terms: 4 + -30x + 5x2 = 2(x + -7) Reorder the terms: 4 + -30x + 5x2 = 2(-7 + x) 4 + -30x + 5x2 = (-7 * 2 + x * 2) 4 + -30x + 5x2 = (-14 + 2x) Solving 4 + -30x + 5x2 = -14 + 2x Solving for variable 'x'. Reorder the terms: 4 + 14 + -30x + -2x + 5x2 = -14 + 2x + 14 + -2x Combine like terms: 4 + 14 = 18 18 + -30x + -2x + 5x2 = -14 + 2x + 14 + -2x Combine like terms: -30x + -2x = -32x 18 + -32x + 5x2 = -14 + 2x + 14 + -2x Reorder the terms: 18 + -32x + 5x2 = -14 + 14 + 2x + -2x Combine like terms: -14 + 14 = 0 18 + -32x + 5x2 = 0 + 2x + -2x 18 + -32x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 18 + -32x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.6 + -6.4x + x2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -6.4x + -3.6 + x2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -6.4x + x2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -6.4x + x2 = 0 + -3.6 -6.4x + x2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -6.4x + x2 = -3.6 The x term is -6.4x. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4x + 10.24 + x2 = -3.6 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = -3.6 + 10.24 Combine like terms: -3.6 + 10.24 = 6.64 10.24 + -6.4x + x2 = 6.64 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 6.64 Calculate the square root of the right side: 2.576819745 Break this problem into two subproblems by setting (x + -3.2) equal to 2.576819745 and -2.576819745.Subproblem 1
x + -3.2 = 2.576819745 Simplifying x + -3.2 = 2.576819745 Reorder the terms: -3.2 + x = 2.576819745 Solving -3.2 + x = 2.576819745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = 2.576819745 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 2.576819745 + 3.2 x = 2.576819745 + 3.2 Combine like terms: 2.576819745 + 3.2 = 5.776819745 x = 5.776819745 Simplifying x = 5.776819745Subproblem 2
x + -3.2 = -2.576819745 Simplifying x + -3.2 = -2.576819745 Reorder the terms: -3.2 + x = -2.576819745 Solving -3.2 + x = -2.576819745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = -2.576819745 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -2.576819745 + 3.2 x = -2.576819745 + 3.2 Combine like terms: -2.576819745 + 3.2 = 0.623180255 x = 0.623180255 Simplifying x = 0.623180255Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.776819745, 0.623180255}
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