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Simplifying -4.9x2 + 42x + -5 = 0 Reorder the terms: -5 + 42x + -4.9x2 = 0 Solving -5 + 42x + -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'. 1.020408163 + -8.571428571x + x2 = 0 Move the constant term to the right: Add '-1.020408163' to each side of the equation. 1.020408163 + -8.571428571x + -1.020408163 + x2 = 0 + -1.020408163 Reorder the terms: 1.020408163 + -1.020408163 + -8.571428571x + x2 = 0 + -1.020408163 Combine like terms: 1.020408163 + -1.020408163 = 0.000000000 0.000000000 + -8.571428571x + x2 = 0 + -1.020408163 -8.571428571x + x2 = 0 + -1.020408163 Combine like terms: 0 + -1.020408163 = -1.020408163 -8.571428571x + x2 = -1.020408163 The x term is -8.571428571x. Take half its coefficient (-4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. -8.571428571x + 18.36734694 + x2 = -1.020408163 + 18.36734694 Reorder the terms: 18.36734694 + -8.571428571x + x2 = -1.020408163 + 18.36734694 Combine like terms: -1.020408163 + 18.36734694 = 17.346938777 18.36734694 + -8.571428571x + x2 = 17.346938777 Factor a perfect square on the left side: (x + -4.285714286)(x + -4.285714286) = 17.346938777 Calculate the square root of the right side: 4.164965639 Break this problem into two subproblems by setting (x + -4.285714286) equal to 4.164965639 and -4.164965639.Subproblem 1
x + -4.285714286 = 4.164965639 Simplifying x + -4.285714286 = 4.164965639 Reorder the terms: -4.285714286 + x = 4.164965639 Solving -4.285714286 + x = 4.164965639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + x = 4.164965639 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x = 4.164965639 + 4.285714286 x = 4.164965639 + 4.285714286 Combine like terms: 4.164965639 + 4.285714286 = 8.450679925 x = 8.450679925 Simplifying x = 8.450679925Subproblem 2
x + -4.285714286 = -4.164965639 Simplifying x + -4.285714286 = -4.164965639 Reorder the terms: -4.285714286 + x = -4.164965639 Solving -4.285714286 + x = -4.164965639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + x = -4.164965639 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x = -4.164965639 + 4.285714286 x = -4.164965639 + 4.285714286 Combine like terms: -4.164965639 + 4.285714286 = 0.120748647 x = 0.120748647 Simplifying x = 0.120748647Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.450679925, 0.120748647}
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