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Simplifying -3 = -4.9x2 + 9.8x + 0 Reorder the terms: -3 = 0 + 9.8x + -4.9x2 Remove the zero: -3 = 9.8x + -4.9x2 Solving -3 = 9.8x + -4.9x2 Solving for variable 'x'. Reorder the terms: -3 + -9.8x + 4.9x2 = 9.8x + -9.8x + -4.9x2 + 4.9x2 Combine like terms: 9.8x + -9.8x = 0.0 -3 + -9.8x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -3 + -9.8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -3 + -9.8x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.612244898 + -2x + x2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -2x + 0.612244898 + x2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -2x + x2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -2x + x2 = 0 + 0.612244898 -2x + x2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -2x + x2 = 0.612244898 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.612244898 + 1 Reorder the terms: 1 + -2x + x2 = 0.612244898 + 1 Combine like terms: 0.612244898 + 1 = 1.612244898 1 + -2x + x2 = 1.612244898 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.612244898 Calculate the square root of the right side: 1.26974206 Break this problem into two subproblems by setting (x + -1) equal to 1.26974206 and -1.26974206.Subproblem 1
x + -1 = 1.26974206 Simplifying x + -1 = 1.26974206 Reorder the terms: -1 + x = 1.26974206 Solving -1 + x = 1.26974206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.26974206 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.26974206 + 1 x = 1.26974206 + 1 Combine like terms: 1.26974206 + 1 = 2.26974206 x = 2.26974206 Simplifying x = 2.26974206Subproblem 2
x + -1 = -1.26974206 Simplifying x + -1 = -1.26974206 Reorder the terms: -1 + x = -1.26974206 Solving -1 + x = -1.26974206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.26974206 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.26974206 + 1 x = -1.26974206 + 1 Combine like terms: -1.26974206 + 1 = -0.26974206 x = -0.26974206 Simplifying x = -0.26974206Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.26974206, -0.26974206}
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