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Simplifying -16(x + -4)(x + 1) = 1.5 Reorder the terms: -16(-4 + x)(x + 1) = 1.5 Reorder the terms: -16(-4 + x)(1 + x) = 1.5 Multiply (-4 + x) * (1 + x) -16(-4(1 + x) + x(1 + x)) = 1.5 -16((1 * -4 + x * -4) + x(1 + x)) = 1.5 -16((-4 + -4x) + x(1 + x)) = 1.5 -16(-4 + -4x + (1 * x + x * x)) = 1.5 -16(-4 + -4x + (1x + x2)) = 1.5 Combine like terms: -4x + 1x = -3x -16(-4 + -3x + x2) = 1.5 (-4 * -16 + -3x * -16 + x2 * -16) = 1.5 (64 + 48x + -16x2) = 1.5 Solving 64 + 48x + -16x2 = 1.5 Solving for variable 'x'. Reorder the terms: 64 + -1.5 + 48x + -16x2 = 1.5 + -1.5 Combine like terms: 64 + -1.5 = 62.5 62.5 + 48x + -16x2 = 1.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 62.5 + 48x + -16x2 = 0.0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -3.90625 + -3x + x2 = 0.0 Move the constant term to the right: Add '3.90625' to each side of the equation. -3.90625 + -3x + 3.90625 + x2 = 0.0 + 3.90625 Reorder the terms: -3.90625 + 3.90625 + -3x + x2 = 0.0 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + -3x + x2 = 0.0 + 3.90625 -3x + x2 = 0.0 + 3.90625 Combine like terms: 0.0 + 3.90625 = 3.90625 -3x + x2 = 3.90625 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 = 3.90625 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 3.90625 + 2.25 Combine like terms: 3.90625 + 2.25 = 6.15625 2.25 + -3x + x2 = 6.15625 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 6.15625 Calculate the square root of the right side: 2.481179155 Break this problem into two subproblems by setting (x + -1.5) equal to 2.481179155 and -2.481179155.Subproblem 1
x + -1.5 = 2.481179155 Simplifying x + -1.5 = 2.481179155 Reorder the terms: -1.5 + x = 2.481179155 Solving -1.5 + x = 2.481179155 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 = 2.481179155 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.481179155 + 1.5 x = 2.481179155 + 1.5 Combine like terms: 2.481179155 + 1.5 = 3.981179155 x = 3.981179155 Simplifying x = 3.981179155Subproblem 2
x + -1.5 = -2.481179155 Simplifying x + -1.5 = -2.481179155 Reorder the terms: -1.5 + x = -2.481179155 Solving -1.5 + x = -2.481179155 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 = -2.481179155 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.481179155 + 1.5 x = -2.481179155 + 1.5 Combine like terms: -2.481179155 + 1.5 = -0.981179155 x = -0.981179155 Simplifying x = -0.981179155Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.981179155, -0.981179155}
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