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Simplifying -4.9x2 + 7x + 400 = 0 Reorder the terms: 400 + 7x + -4.9x2 = 0 Solving 400 + 7x + -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'. -81.63265306 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '81.63265306' to each side of the equation. -81.63265306 + -1.428571429x + 81.63265306 + x2 = 0 + 81.63265306 Reorder the terms: -81.63265306 + 81.63265306 + -1.428571429x + x2 = 0 + 81.63265306 Combine like terms: -81.63265306 + 81.63265306 = 0.00000000 0.00000000 + -1.428571429x + x2 = 0 + 81.63265306 -1.428571429x + x2 = 0 + 81.63265306 Combine like terms: 0 + 81.63265306 = 81.63265306 -1.428571429x + x2 = 81.63265306 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 81.63265306 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 81.63265306 + 0.5102040819 Combine like terms: 81.63265306 + 0.5102040819 = 82.1428571419 0.5102040819 + -1.428571429x + x2 = 82.1428571419 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 82.1428571419 Calculate the square root of the right side: 9.063269672 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 9.063269672 and -9.063269672.Subproblem 1
x + -0.7142857145 = 9.063269672 Simplifying x + -0.7142857145 = 9.063269672 Reorder the terms: -0.7142857145 + x = 9.063269672 Solving -0.7142857145 + x = 9.063269672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 9.063269672 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 9.063269672 + 0.7142857145 x = 9.063269672 + 0.7142857145 Combine like terms: 9.063269672 + 0.7142857145 = 9.7775553865 x = 9.7775553865 Simplifying x = 9.7775553865Subproblem 2
x + -0.7142857145 = -9.063269672 Simplifying x + -0.7142857145 = -9.063269672 Reorder the terms: -0.7142857145 + x = -9.063269672 Solving -0.7142857145 + x = -9.063269672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -9.063269672 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -9.063269672 + 0.7142857145 x = -9.063269672 + 0.7142857145 Combine like terms: -9.063269672 + 0.7142857145 = -8.3489839575 x = -8.3489839575 Simplifying x = -8.3489839575Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.7775553865, -8.3489839575}
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