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Simplifying w2 + 6w + 15 = 53 Reorder the terms: 15 + 6w + w2 = 53 Solving 15 + 6w + w2 = 53 Solving for variable 'w'. Reorder the terms: 15 + -53 + 6w + w2 = 53 + -53 Combine like terms: 15 + -53 = -38 -38 + 6w + w2 = 53 + -53 Combine like terms: 53 + -53 = 0 -38 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 6w + 38 + w2 = 0 + 38 Reorder the terms: -38 + 38 + 6w + w2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 6w + w2 = 0 + 38 6w + w2 = 0 + 38 Combine like terms: 0 + 38 = 38 6w + w2 = 38 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 = 38 + 9 Reorder the terms: 9 + 6w + w2 = 38 + 9 Combine like terms: 38 + 9 = 47 9 + 6w + w2 = 47 Factor a perfect square on the left side: (w + 3)(w + 3) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (w + 3) equal to 6.8556546 and -6.8556546.Subproblem 1
w + 3 = 6.8556546 Simplifying w + 3 = 6.8556546 Reorder the terms: 3 + w = 6.8556546 Solving 3 + w = 6.8556546 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 = 6.8556546 + -3 Combine like terms: 3 + -3 = 0 0 + w = 6.8556546 + -3 w = 6.8556546 + -3 Combine like terms: 6.8556546 + -3 = 3.8556546 w = 3.8556546 Simplifying w = 3.8556546Subproblem 2
w + 3 = -6.8556546 Simplifying w + 3 = -6.8556546 Reorder the terms: 3 + w = -6.8556546 Solving 3 + w = -6.8556546 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 = -6.8556546 + -3 Combine like terms: 3 + -3 = 0 0 + w = -6.8556546 + -3 w = -6.8556546 + -3 Combine like terms: -6.8556546 + -3 = -9.8556546 w = -9.8556546 Simplifying w = -9.8556546Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.8556546, -9.8556546}
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