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Simplifying 5x(x + -2) + 3 = 6(x + 3) + -4x Reorder the terms: 5x(-2 + x) + 3 = 6(x + 3) + -4x (-2 * 5x + x * 5x) + 3 = 6(x + 3) + -4x (-10x + 5x2) + 3 = 6(x + 3) + -4x Reorder the terms: 3 + -10x + 5x2 = 6(x + 3) + -4x Reorder the terms: 3 + -10x + 5x2 = 6(3 + x) + -4x 3 + -10x + 5x2 = (3 * 6 + x * 6) + -4x 3 + -10x + 5x2 = (18 + 6x) + -4x Combine like terms: 6x + -4x = 2x 3 + -10x + 5x2 = 18 + 2x Solving 3 + -10x + 5x2 = 18 + 2x Solving for variable 'x'. Reorder the terms: 3 + -18 + -10x + -2x + 5x2 = 18 + 2x + -18 + -2x Combine like terms: 3 + -18 = -15 -15 + -10x + -2x + 5x2 = 18 + 2x + -18 + -2x Combine like terms: -10x + -2x = -12x -15 + -12x + 5x2 = 18 + 2x + -18 + -2x Reorder the terms: -15 + -12x + 5x2 = 18 + -18 + 2x + -2x Combine like terms: 18 + -18 = 0 -15 + -12x + 5x2 = 0 + 2x + -2x -15 + -12x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -15 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + -2.4x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -2.4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.4x + x2 = 0 + 3 -2.4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.4x + x2 = 3 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 3 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 3 + 1.44 Combine like terms: 3 + 1.44 = 4.44 1.44 + -2.4x + x2 = 4.44 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 4.44 Calculate the square root of the right side: 2.107130751 Break this problem into two subproblems by setting (x + -1.2) equal to 2.107130751 and -2.107130751.Subproblem 1
x + -1.2 = 2.107130751 Simplifying x + -1.2 = 2.107130751 Reorder the terms: -1.2 + x = 2.107130751 Solving -1.2 + x = 2.107130751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 2.107130751 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 2.107130751 + 1.2 x = 2.107130751 + 1.2 Combine like terms: 2.107130751 + 1.2 = 3.307130751 x = 3.307130751 Simplifying x = 3.307130751Subproblem 2
x + -1.2 = -2.107130751 Simplifying x + -1.2 = -2.107130751 Reorder the terms: -1.2 + x = -2.107130751 Solving -1.2 + x = -2.107130751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -2.107130751 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -2.107130751 + 1.2 x = -2.107130751 + 1.2 Combine like terms: -2.107130751 + 1.2 = -0.907130751 x = -0.907130751 Simplifying x = -0.907130751Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.307130751, -0.907130751}
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