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Simplifying 5w2 + -3w + -20 = 0 Reorder the terms: -20 + -3w + 5w2 = 0 Solving -20 + -3w + 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'. -4 + -0.6w + w2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.6w + 4 + w2 = 0 + 4 Reorder the terms: -4 + 4 + -0.6w + w2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.6w + w2 = 0 + 4 -0.6w + w2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.6w + w2 = 4 The w term is -0.6w. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6w + 0.09 + w2 = 4 + 0.09 Reorder the terms: 0.09 + -0.6w + w2 = 4 + 0.09 Combine like terms: 4 + 0.09 = 4.09 0.09 + -0.6w + w2 = 4.09 Factor a perfect square on the left side: (w + -0.3)(w + -0.3) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (w + -0.3) equal to 2.022374842 and -2.022374842.Subproblem 1
w + -0.3 = 2.022374842 Simplifying w + -0.3 = 2.022374842 Reorder the terms: -0.3 + w = 2.022374842 Solving -0.3 + w = 2.022374842 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + w = 2.022374842 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + w = 2.022374842 + 0.3 w = 2.022374842 + 0.3 Combine like terms: 2.022374842 + 0.3 = 2.322374842 w = 2.322374842 Simplifying w = 2.322374842Subproblem 2
w + -0.3 = -2.022374842 Simplifying w + -0.3 = -2.022374842 Reorder the terms: -0.3 + w = -2.022374842 Solving -0.3 + w = -2.022374842 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + w = -2.022374842 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + w = -2.022374842 + 0.3 w = -2.022374842 + 0.3 Combine like terms: -2.022374842 + 0.3 = -1.722374842 w = -1.722374842 Simplifying w = -1.722374842Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.322374842, -1.722374842}
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