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Simplifying 7 + -4(w + -2) * w = 0 Reorder the terms: 7 + -4(-2 + w) * w = 0 Reorder the terms for easier multiplication: 7 + -4w(-2 + w) = 0 7 + (-2 * -4w + w * -4w) = 0 7 + (8w + -4w2) = 0 Solving 7 + 8w + -4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -2w + w2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -2w + 1.75 + w2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -2w + w2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -2w + w2 = 0 + 1.75 -2w + w2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -2w + w2 = 1.75 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 1.75 + 1 Reorder the terms: 1 + -2w + w2 = 1.75 + 1 Combine like terms: 1.75 + 1 = 2.75 1 + -2w + w2 = 2.75 Factor a perfect square on the left side: (w + -1)(w + -1) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (w + -1) equal to 1.658312395 and -1.658312395.Subproblem 1
w + -1 = 1.658312395 Simplifying w + -1 = 1.658312395 Reorder the terms: -1 + w = 1.658312395 Solving -1 + w = 1.658312395 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 1.658312395 + 1 Combine like terms: -1 + 1 = 0 0 + w = 1.658312395 + 1 w = 1.658312395 + 1 Combine like terms: 1.658312395 + 1 = 2.658312395 w = 2.658312395 Simplifying w = 2.658312395Subproblem 2
w + -1 = -1.658312395 Simplifying w + -1 = -1.658312395 Reorder the terms: -1 + w = -1.658312395 Solving -1 + w = -1.658312395 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -1.658312395 + 1 Combine like terms: -1 + 1 = 0 0 + w = -1.658312395 + 1 w = -1.658312395 + 1 Combine like terms: -1.658312395 + 1 = -0.658312395 w = -0.658312395 Simplifying w = -0.658312395Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.658312395, -0.658312395}
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