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Simplifying 0.42w * 0.42w + -0.04w = 0.28 Reorder the terms for easier multiplication: 0.42 * 0.42w * w + -0.04w = 0.28 Multiply 0.42 * 0.42 0.1764w * w + -0.04w = 0.28 Multiply w * w 0.1764w2 + -0.04w = 0.28 Reorder the terms: -0.04w + 0.1764w2 = 0.28 Solving -0.04w + 0.1764w2 = 0.28 Solving for variable 'w'. Reorder the terms: -0.28 + -0.04w + 0.1764w2 = 0.28 + -0.28 Combine like terms: 0.28 + -0.28 = 0.00 -0.28 + -0.04w + 0.1764w2 = 0.00 Begin completing the square. Divide all terms by 0.1764 the coefficient of the squared term: Divide each side by '0.1764'. -1.587301587 + -0.2267573696w + w2 = 0 Move the constant term to the right: Add '1.587301587' to each side of the equation. -1.587301587 + -0.2267573696w + 1.587301587 + w2 = 0 + 1.587301587 Reorder the terms: -1.587301587 + 1.587301587 + -0.2267573696w + w2 = 0 + 1.587301587 Combine like terms: -1.587301587 + 1.587301587 = 0.000000000 0.000000000 + -0.2267573696w + w2 = 0 + 1.587301587 -0.2267573696w + w2 = 0 + 1.587301587 Combine like terms: 0 + 1.587301587 = 1.587301587 -0.2267573696w + w2 = 1.587301587 The w term is -0.2267573696w. Take half its coefficient (-0.1133786848). Square it (0.01285472617) and add it to both sides. Add '0.01285472617' to each side of the equation. -0.2267573696w + 0.01285472617 + w2 = 1.587301587 + 0.01285472617 Reorder the terms: 0.01285472617 + -0.2267573696w + w2 = 1.587301587 + 0.01285472617 Combine like terms: 1.587301587 + 0.01285472617 = 1.60015631317 0.01285472617 + -0.2267573696w + w2 = 1.60015631317 Factor a perfect square on the left side: (w + -0.1133786848)(w + -0.1133786848) = 1.60015631317 Calculate the square root of the right side: 1.264972851 Break this problem into two subproblems by setting (w + -0.1133786848) equal to 1.264972851 and -1.264972851.Subproblem 1
w + -0.1133786848 = 1.264972851 Simplifying w + -0.1133786848 = 1.264972851 Reorder the terms: -0.1133786848 + w = 1.264972851 Solving -0.1133786848 + w = 1.264972851 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1133786848' to each side of the equation. -0.1133786848 + 0.1133786848 + w = 1.264972851 + 0.1133786848 Combine like terms: -0.1133786848 + 0.1133786848 = 0.0000000000 0.0000000000 + w = 1.264972851 + 0.1133786848 w = 1.264972851 + 0.1133786848 Combine like terms: 1.264972851 + 0.1133786848 = 1.3783515358 w = 1.3783515358 Simplifying w = 1.3783515358Subproblem 2
w + -0.1133786848 = -1.264972851 Simplifying w + -0.1133786848 = -1.264972851 Reorder the terms: -0.1133786848 + w = -1.264972851 Solving -0.1133786848 + w = -1.264972851 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1133786848' to each side of the equation. -0.1133786848 + 0.1133786848 + w = -1.264972851 + 0.1133786848 Combine like terms: -0.1133786848 + 0.1133786848 = 0.0000000000 0.0000000000 + w = -1.264972851 + 0.1133786848 w = -1.264972851 + 0.1133786848 Combine like terms: -1.264972851 + 0.1133786848 = -1.1515941662 w = -1.1515941662 Simplifying w = -1.1515941662Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.3783515358, -1.1515941662}
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