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Simplifying 5(x + -4) * 3x = 4 Reorder the terms: 5(-4 + x) * 3x = 4 Reorder the terms for easier multiplication: 5 * 3x(-4 + x) = 4 Multiply 5 * 3 15x(-4 + x) = 4 (-4 * 15x + x * 15x) = 4 (-60x + 15x2) = 4 Solving -60x + 15x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -60x + 15x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -60x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2666666667 + -4x + x2 = 0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + -4x + 0.2666666667 + x2 = 0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + -4x + x2 = 0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + 0.2666666667 -4x + x2 = 0 + 0.2666666667 Combine like terms: 0 + 0.2666666667 = 0.2666666667 -4x + x2 = 0.2666666667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 0.2666666667 + 4 Reorder the terms: 4 + -4x + x2 = 0.2666666667 + 4 Combine like terms: 0.2666666667 + 4 = 4.2666666667 4 + -4x + x2 = 4.2666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.2666666667 Calculate the square root of the right side: 2.065591118 Break this problem into two subproblems by setting (x + -2) equal to 2.065591118 and -2.065591118.Subproblem 1
x + -2 = 2.065591118 Simplifying x + -2 = 2.065591118 Reorder the terms: -2 + x = 2.065591118 Solving -2 + x = 2.065591118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.065591118 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.065591118 + 2 x = 2.065591118 + 2 Combine like terms: 2.065591118 + 2 = 4.065591118 x = 4.065591118 Simplifying x = 4.065591118Subproblem 2
x + -2 = -2.065591118 Simplifying x + -2 = -2.065591118 Reorder the terms: -2 + x = -2.065591118 Solving -2 + x = -2.065591118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.065591118 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.065591118 + 2 x = -2.065591118 + 2 Combine like terms: -2.065591118 + 2 = -0.065591118 x = -0.065591118 Simplifying x = -0.065591118Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.065591118, -0.065591118}
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