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Simplifying 4w2 + -24w + -7 = 0 Reorder the terms: -7 + -24w + 4w2 = 0 Solving -7 + -24w + 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 + -6w + w2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -6w + 1.75 + w2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -6w + w2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -6w + w2 = 0 + 1.75 -6w + w2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -6w + w2 = 1.75 The w term is -6w. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6w + 9 + w2 = 1.75 + 9 Reorder the terms: 9 + -6w + w2 = 1.75 + 9 Combine like terms: 1.75 + 9 = 10.75 9 + -6w + w2 = 10.75 Factor a perfect square on the left side: (w + -3)(w + -3) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (w + -3) equal to 3.278719262 and -3.278719262.Subproblem 1
w + -3 = 3.278719262 Simplifying w + -3 = 3.278719262 Reorder the terms: -3 + w = 3.278719262 Solving -3 + w = 3.278719262 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = 3.278719262 + 3 Combine like terms: -3 + 3 = 0 0 + w = 3.278719262 + 3 w = 3.278719262 + 3 Combine like terms: 3.278719262 + 3 = 6.278719262 w = 6.278719262 Simplifying w = 6.278719262Subproblem 2
w + -3 = -3.278719262 Simplifying w + -3 = -3.278719262 Reorder the terms: -3 + w = -3.278719262 Solving -3 + w = -3.278719262 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = -3.278719262 + 3 Combine like terms: -3 + 3 = 0 0 + w = -3.278719262 + 3 w = -3.278719262 + 3 Combine like terms: -3.278719262 + 3 = -0.278719262 w = -0.278719262 Simplifying w = -0.278719262Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.278719262, -0.278719262}
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