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Simplifying -0.2(x + 22)(x + -15) = 0 Reorder the terms: -0.2(22 + x)(x + -15) = 0 Reorder the terms: -0.2(22 + x)(-15 + x) = 0 Multiply (22 + x) * (-15 + x) -0.2(22(-15 + x) + x(-15 + x)) = 0 -0.2((-15 * 22 + x * 22) + x(-15 + x)) = 0 -0.2((-330 + 22x) + x(-15 + x)) = 0 -0.2(-330 + 22x + (-15 * x + x * x)) = 0 -0.2(-330 + 22x + (-15x + x2)) = 0 Combine like terms: 22x + -15x = 7x -0.2(-330 + 7x + x2) = 0 (-330 * -0.2 + 7x * -0.2 + x2 * -0.2) = 0 (66 + -1.4x + -0.2x2) = 0 Solving 66 + -1.4x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -330 + 7x + x2 = 0 Move the constant term to the right: Add '330' to each side of the equation. -330 + 7x + 330 + x2 = 0 + 330 Reorder the terms: -330 + 330 + 7x + x2 = 0 + 330 Combine like terms: -330 + 330 = 0 0 + 7x + x2 = 0 + 330 7x + x2 = 0 + 330 Combine like terms: 0 + 330 = 330 7x + x2 = 330 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 330 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 330 + 12.25 Combine like terms: 330 + 12.25 = 342.25 12.25 + 7x + x2 = 342.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 342.25 Calculate the square root of the right side: 18.5 Break this problem into two subproblems by setting (x + 3.5) equal to 18.5 and -18.5.Subproblem 1
x + 3.5 = 18.5 Simplifying x + 3.5 = 18.5 Reorder the terms: 3.5 + x = 18.5 Solving 3.5 + x = 18.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 18.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 18.5 + -3.5 x = 18.5 + -3.5 Combine like terms: 18.5 + -3.5 = 15 x = 15 Simplifying x = 15Subproblem 2
x + 3.5 = -18.5 Simplifying x + 3.5 = -18.5 Reorder the terms: 3.5 + x = -18.5 Solving 3.5 + x = -18.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -18.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -18.5 + -3.5 x = -18.5 + -3.5 Combine like terms: -18.5 + -3.5 = -22 x = -22 Simplifying x = -22Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, -22}
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