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Simplifying -2.4(x + 5)(x + -7) = 0 Reorder the terms: -2.4(5 + x)(x + -7) = 0 Reorder the terms: -2.4(5 + x)(-7 + x) = 0 Multiply (5 + x) * (-7 + x) -2.4(5(-7 + x) + x(-7 + x)) = 0 -2.4((-7 * 5 + x * 5) + x(-7 + x)) = 0 -2.4((-35 + 5x) + x(-7 + x)) = 0 -2.4(-35 + 5x + (-7 * x + x * x)) = 0 -2.4(-35 + 5x + (-7x + x2)) = 0 Combine like terms: 5x + -7x = -2x -2.4(-35 + -2x + x2) = 0 (-35 * -2.4 + -2x * -2.4 + x2 * -2.4) = 0 (84 + 4.8x + -2.4x2) = 0 Solving 84 + 4.8x + -2.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.4 the coefficient of the squared term: Divide each side by '-2.4'. -35 + -2x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -2x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -2x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -2x + x2 = 0 + 35 -2x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -2x + x2 = 35 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 35 + 1 Reorder the terms: 1 + -2x + x2 = 35 + 1 Combine like terms: 35 + 1 = 36 1 + -2x + x2 = 36 Factor a perfect square on the left side: (x + -1)(x + -1) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + -1) equal to 6 and -6.Subproblem 1
x + -1 = 6 Simplifying x + -1 = 6 Reorder the terms: -1 + x = 6 Solving -1 + x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 6 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6 + 1 x = 6 + 1 Combine like terms: 6 + 1 = 7 x = 7 Simplifying x = 7Subproblem 2
x + -1 = -6 Simplifying x + -1 = -6 Reorder the terms: -1 + x = -6 Solving -1 + x = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -6 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6 + 1 x = -6 + 1 Combine like terms: -6 + 1 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {7, -5}
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