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Simplifying 4x(x + -5) + -3(x + 6) = 0 Reorder the terms: 4x(-5 + x) + -3(x + 6) = 0 (-5 * 4x + x * 4x) + -3(x + 6) = 0 (-20x + 4x2) + -3(x + 6) = 0 Reorder the terms: -20x + 4x2 + -3(6 + x) = 0 -20x + 4x2 + (6 * -3 + x * -3) = 0 -20x + 4x2 + (-18 + -3x) = 0 Reorder the terms: -18 + -20x + -3x + 4x2 = 0 Combine like terms: -20x + -3x = -23x -18 + -23x + 4x2 = 0 Solving -18 + -23x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + -5.75x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -5.75x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -5.75x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -5.75x + x2 = 0 + 4.5 -5.75x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -5.75x + x2 = 4.5 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = 4.5 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 4.5 + 8.265625 Combine like terms: 4.5 + 8.265625 = 12.765625 8.265625 + -5.75x + x2 = 12.765625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 12.765625 Calculate the square root of the right side: 3.572901482 Break this problem into two subproblems by setting (x + -2.875) equal to 3.572901482 and -3.572901482.Subproblem 1
x + -2.875 = 3.572901482 Simplifying x + -2.875 = 3.572901482 Reorder the terms: -2.875 + x = 3.572901482 Solving -2.875 + x = 3.572901482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 3.572901482 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 3.572901482 + 2.875 x = 3.572901482 + 2.875 Combine like terms: 3.572901482 + 2.875 = 6.447901482 x = 6.447901482 Simplifying x = 6.447901482Subproblem 2
x + -2.875 = -3.572901482 Simplifying x + -2.875 = -3.572901482 Reorder the terms: -2.875 + x = -3.572901482 Solving -2.875 + x = -3.572901482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -3.572901482 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -3.572901482 + 2.875 x = -3.572901482 + 2.875 Combine like terms: -3.572901482 + 2.875 = -0.697901482 x = -0.697901482 Simplifying x = -0.697901482Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.447901482, -0.697901482}
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