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Simplifying 4x(x + -6) + 3x(x + 1) = 4 Reorder the terms: 4x(-6 + x) + 3x(x + 1) = 4 (-6 * 4x + x * 4x) + 3x(x + 1) = 4 (-24x + 4x2) + 3x(x + 1) = 4 Reorder the terms: -24x + 4x2 + 3x(1 + x) = 4 -24x + 4x2 + (1 * 3x + x * 3x) = 4 -24x + 4x2 + (3x + 3x2) = 4 Reorder the terms: -24x + 3x + 4x2 + 3x2 = 4 Combine like terms: -24x + 3x = -21x -21x + 4x2 + 3x2 = 4 Combine like terms: 4x2 + 3x2 = 7x2 -21x + 7x2 = 4 Solving -21x + 7x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -21x + 7x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -21x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + -3x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -3x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -3x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + 0.5714285714 -3x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -3x + x2 = 0.5714285714 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.5714285714 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.5714285714 + 2.25 Combine like terms: 0.5714285714 + 2.25 = 2.8214285714 2.25 + -3x + x2 = 2.8214285714 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.8214285714 Calculate the square root of the right side: 1.679710859 Break this problem into two subproblems by setting (x + -1.5) equal to 1.679710859 and -1.679710859.Subproblem 1
x + -1.5 = 1.679710859 Simplifying x + -1.5 = 1.679710859 Reorder the terms: -1.5 + x = 1.679710859 Solving -1.5 + x = 1.679710859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.679710859 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.679710859 + 1.5 x = 1.679710859 + 1.5 Combine like terms: 1.679710859 + 1.5 = 3.179710859 x = 3.179710859 Simplifying x = 3.179710859Subproblem 2
x + -1.5 = -1.679710859 Simplifying x + -1.5 = -1.679710859 Reorder the terms: -1.5 + x = -1.679710859 Solving -1.5 + x = -1.679710859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.679710859 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.679710859 + 1.5 x = -1.679710859 + 1.5 Combine like terms: -1.679710859 + 1.5 = -0.179710859 x = -0.179710859 Simplifying x = -0.179710859Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.179710859, -0.179710859}
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