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Simplifying -4.9x2 + 22.5x + 4 = 0 Reorder the terms: 4 + 22.5x + -4.9x2 = 0 Solving 4 + 22.5x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.8163265306 + -4.591836735x + x2 = 0 Move the constant term to the right: Add '0.8163265306' to each side of the equation. -0.8163265306 + -4.591836735x + 0.8163265306 + x2 = 0 + 0.8163265306 Reorder the terms: -0.8163265306 + 0.8163265306 + -4.591836735x + x2 = 0 + 0.8163265306 Combine like terms: -0.8163265306 + 0.8163265306 = 0.0000000000 0.0000000000 + -4.591836735x + x2 = 0 + 0.8163265306 -4.591836735x + x2 = 0 + 0.8163265306 Combine like terms: 0 + 0.8163265306 = 0.8163265306 -4.591836735x + x2 = 0.8163265306 The x term is -4.591836735x. Take half its coefficient (-2.295918368). Square it (5.271241153) and add it to both sides. Add '5.271241153' to each side of the equation. -4.591836735x + 5.271241153 + x2 = 0.8163265306 + 5.271241153 Reorder the terms: 5.271241153 + -4.591836735x + x2 = 0.8163265306 + 5.271241153 Combine like terms: 0.8163265306 + 5.271241153 = 6.0875676836 5.271241153 + -4.591836735x + x2 = 6.0875676836 Factor a perfect square on the left side: (x + -2.295918368)(x + -2.295918368) = 6.0875676836 Calculate the square root of the right side: 2.467299674 Break this problem into two subproblems by setting (x + -2.295918368) equal to 2.467299674 and -2.467299674.Subproblem 1
x + -2.295918368 = 2.467299674 Simplifying x + -2.295918368 = 2.467299674 Reorder the terms: -2.295918368 + x = 2.467299674 Solving -2.295918368 + x = 2.467299674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.295918368' to each side of the equation. -2.295918368 + 2.295918368 + x = 2.467299674 + 2.295918368 Combine like terms: -2.295918368 + 2.295918368 = 0.000000000 0.000000000 + x = 2.467299674 + 2.295918368 x = 2.467299674 + 2.295918368 Combine like terms: 2.467299674 + 2.295918368 = 4.763218042 x = 4.763218042 Simplifying x = 4.763218042Subproblem 2
x + -2.295918368 = -2.467299674 Simplifying x + -2.295918368 = -2.467299674 Reorder the terms: -2.295918368 + x = -2.467299674 Solving -2.295918368 + x = -2.467299674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.295918368' to each side of the equation. -2.295918368 + 2.295918368 + x = -2.467299674 + 2.295918368 Combine like terms: -2.295918368 + 2.295918368 = 0.000000000 0.000000000 + x = -2.467299674 + 2.295918368 x = -2.467299674 + 2.295918368 Combine like terms: -2.467299674 + 2.295918368 = -0.171381306 x = -0.171381306 Simplifying x = -0.171381306Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.763218042, -0.171381306}
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