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Simplifying -4.9x2 + 23.5x + 3 = 0 Reorder the terms: 3 + 23.5x + -4.9x2 = 0 Solving 3 + 23.5x + -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'. -0.612244898 + -4.795918367x + x2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -4.795918367x + 0.612244898 + x2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -4.795918367x + x2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -4.795918367x + x2 = 0 + 0.612244898 -4.795918367x + x2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -4.795918367x + x2 = 0.612244898 The x term is -4.795918367x. Take half its coefficient (-2.397959184). Square it (5.750208248) and add it to both sides. Add '5.750208248' to each side of the equation. -4.795918367x + 5.750208248 + x2 = 0.612244898 + 5.750208248 Reorder the terms: 5.750208248 + -4.795918367x + x2 = 0.612244898 + 5.750208248 Combine like terms: 0.612244898 + 5.750208248 = 6.362453146 5.750208248 + -4.795918367x + x2 = 6.362453146 Factor a perfect square on the left side: (x + -2.397959184)(x + -2.397959184) = 6.362453146 Calculate the square root of the right side: 2.522390364 Break this problem into two subproblems by setting (x + -2.397959184) equal to 2.522390364 and -2.522390364.Subproblem 1
x + -2.397959184 = 2.522390364 Simplifying x + -2.397959184 = 2.522390364 Reorder the terms: -2.397959184 + x = 2.522390364 Solving -2.397959184 + x = 2.522390364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.397959184' to each side of the equation. -2.397959184 + 2.397959184 + x = 2.522390364 + 2.397959184 Combine like terms: -2.397959184 + 2.397959184 = 0.000000000 0.000000000 + x = 2.522390364 + 2.397959184 x = 2.522390364 + 2.397959184 Combine like terms: 2.522390364 + 2.397959184 = 4.920349548 x = 4.920349548 Simplifying x = 4.920349548Subproblem 2
x + -2.397959184 = -2.522390364 Simplifying x + -2.397959184 = -2.522390364 Reorder the terms: -2.397959184 + x = -2.522390364 Solving -2.397959184 + x = -2.522390364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.397959184' to each side of the equation. -2.397959184 + 2.397959184 + x = -2.522390364 + 2.397959184 Combine like terms: -2.397959184 + 2.397959184 = 0.000000000 0.000000000 + x = -2.522390364 + 2.397959184 x = -2.522390364 + 2.397959184 Combine like terms: -2.522390364 + 2.397959184 = -0.12443118 x = -0.12443118 Simplifying x = -0.12443118Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.920349548, -0.12443118}
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