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Simplifying 5w2 + 7w + -36 = 0 Reorder the terms: -36 + 7w + 5w2 = 0 Solving -36 + 7w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + 1.4w + w2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 1.4w + 7.2 + w2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 1.4w + w2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 1.4w + w2 = 0 + 7.2 1.4w + w2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 1.4w + w2 = 7.2 The w term is 1.4w. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4w + 0.49 + w2 = 7.2 + 0.49 Reorder the terms: 0.49 + 1.4w + w2 = 7.2 + 0.49 Combine like terms: 7.2 + 0.49 = 7.69 0.49 + 1.4w + w2 = 7.69 Factor a perfect square on the left side: (w + 0.7)(w + 0.7) = 7.69 Calculate the square root of the right side: 2.773084925 Break this problem into two subproblems by setting (w + 0.7) equal to 2.773084925 and -2.773084925.Subproblem 1
w + 0.7 = 2.773084925 Simplifying w + 0.7 = 2.773084925 Reorder the terms: 0.7 + w = 2.773084925 Solving 0.7 + w = 2.773084925 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + w = 2.773084925 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + w = 2.773084925 + -0.7 w = 2.773084925 + -0.7 Combine like terms: 2.773084925 + -0.7 = 2.073084925 w = 2.073084925 Simplifying w = 2.073084925Subproblem 2
w + 0.7 = -2.773084925 Simplifying w + 0.7 = -2.773084925 Reorder the terms: 0.7 + w = -2.773084925 Solving 0.7 + w = -2.773084925 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + w = -2.773084925 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + w = -2.773084925 + -0.7 w = -2.773084925 + -0.7 Combine like terms: -2.773084925 + -0.7 = -3.473084925 w = -3.473084925 Simplifying w = -3.473084925Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.073084925, -3.473084925}
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