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Simplifying 8(w + -7)(-4w + -4) = 3w Reorder the terms: 8(-7 + w)(-4w + -4) = 3w Reorder the terms: 8(-7 + w)(-4 + -4w) = 3w Multiply (-7 + w) * (-4 + -4w) 8(-7(-4 + -4w) + w(-4 + -4w)) = 3w 8((-4 * -7 + -4w * -7) + w(-4 + -4w)) = 3w 8((28 + 28w) + w(-4 + -4w)) = 3w 8(28 + 28w + (-4 * w + -4w * w)) = 3w 8(28 + 28w + (-4w + -4w2)) = 3w Combine like terms: 28w + -4w = 24w 8(28 + 24w + -4w2) = 3w (28 * 8 + 24w * 8 + -4w2 * 8) = 3w (224 + 192w + -32w2) = 3w Solving 224 + 192w + -32w2 = 3w Solving for variable 'w'. Reorder the terms: 224 + 192w + -3w + -32w2 = 3w + -3w Combine like terms: 192w + -3w = 189w 224 + 189w + -32w2 = 3w + -3w Combine like terms: 3w + -3w = 0 224 + 189w + -32w2 = 0 Begin completing the square. Divide all terms by -32 the coefficient of the squared term: Divide each side by '-32'. -7 + -5.90625w + w2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -5.90625w + 7 + w2 = 0 + 7 Reorder the terms: -7 + 7 + -5.90625w + w2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5.90625w + w2 = 0 + 7 -5.90625w + w2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5.90625w + w2 = 7 The w term is -5.90625w. Take half its coefficient (-2.953125). Square it (8.720947266) and add it to both sides. Add '8.720947266' to each side of the equation. -5.90625w + 8.720947266 + w2 = 7 + 8.720947266 Reorder the terms: 8.720947266 + -5.90625w + w2 = 7 + 8.720947266 Combine like terms: 7 + 8.720947266 = 15.720947266 8.720947266 + -5.90625w + w2 = 15.720947266 Factor a perfect square on the left side: (w + -2.953125)(w + -2.953125) = 15.720947266 Calculate the square root of the right side: 3.964964977 Break this problem into two subproblems by setting (w + -2.953125) equal to 3.964964977 and -3.964964977.Subproblem 1
w + -2.953125 = 3.964964977 Simplifying w + -2.953125 = 3.964964977 Reorder the terms: -2.953125 + w = 3.964964977 Solving -2.953125 + w = 3.964964977 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.953125' to each side of the equation. -2.953125 + 2.953125 + w = 3.964964977 + 2.953125 Combine like terms: -2.953125 + 2.953125 = 0.000000 0.000000 + w = 3.964964977 + 2.953125 w = 3.964964977 + 2.953125 Combine like terms: 3.964964977 + 2.953125 = 6.918089977 w = 6.918089977 Simplifying w = 6.918089977Subproblem 2
w + -2.953125 = -3.964964977 Simplifying w + -2.953125 = -3.964964977 Reorder the terms: -2.953125 + w = -3.964964977 Solving -2.953125 + w = -3.964964977 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.953125' to each side of the equation. -2.953125 + 2.953125 + w = -3.964964977 + 2.953125 Combine like terms: -2.953125 + 2.953125 = 0.000000 0.000000 + w = -3.964964977 + 2.953125 w = -3.964964977 + 2.953125 Combine like terms: -3.964964977 + 2.953125 = -1.011839977 w = -1.011839977 Simplifying w = -1.011839977Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.918089977, -1.011839977}
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